YES Problem: 0(1(2(3(x1)))) -> 0(4(2(x1))) 2(0(5(4(5(x1))))) -> 0(3(2(5(x1)))) 1(2(3(2(3(1(x1)))))) -> 2(4(2(0(2(x1))))) 3(5(2(1(2(2(x1)))))) -> 2(5(5(5(x1)))) 5(1(0(4(1(3(x1)))))) -> 5(4(5(2(0(x1))))) 0(3(1(4(0(1(2(x1))))))) -> 0(0(0(3(2(1(5(x1))))))) 1(1(5(5(4(4(4(2(x1)))))))) -> 1(0(1(1(3(2(0(5(x1)))))))) 2(0(2(0(3(5(1(5(x1)))))))) -> 2(5(1(0(5(0(1(0(x1)))))))) 3(5(1(2(3(1(0(1(0(x1))))))))) -> 5(3(5(1(2(4(3(x1))))))) 1(1(0(5(3(5(1(5(1(5(x1)))))))))) -> 1(5(0(2(0(2(2(1(1(3(3(x1))))))))))) 2(2(1(2(4(2(0(5(0(4(x1)))))))))) -> 3(2(1(1(3(2(3(5(0(4(x1)))))))))) 1(0(5(0(5(4(1(3(2(4(1(x1))))))))))) -> 3(5(4(3(4(5(3(0(5(x1))))))))) 0(1(1(1(2(2(1(5(1(0(3(5(x1)))))))))))) -> 0(0(1(0(2(3(0(0(1(5(1(2(0(x1))))))))))))) 2(5(4(3(5(3(3(2(4(0(4(3(x1)))))))))))) -> 5(3(2(3(1(0(5(4(0(4(2(5(x1)))))))))))) 3(3(1(5(0(2(5(2(4(3(1(5(x1)))))))))))) -> 5(0(0(4(4(2(1(5(0(1(0(0(0(0(x1)))))))))))))) 1(5(2(2(0(5(2(3(4(4(3(3(5(3(x1)))))))))))))) -> 2(5(2(1(0(3(1(2(3(4(5(4(4(0(x1)))))))))))))) 3(2(3(3(0(2(3(5(4(2(3(3(2(3(x1)))))))))))))) -> 5(5(3(5(5(3(5(2(4(0(1(0(0(x1))))))))))))) 3(4(3(2(5(1(1(5(5(3(0(0(2(0(x1)))))))))))))) -> 4(1(0(1(3(0(0(4(4(5(1(2(4(2(x1)))))))))))))) 2(0(1(0(3(2(5(2(1(3(5(1(0(1(3(x1))))))))))))))) -> 0(0(5(3(2(3(1(3(1(3(2(0(3(2(x1)))))))))))))) 0(2(5(2(0(5(3(2(4(3(5(1(4(4(4(5(x1)))))))))))))))) -> 2(4(4(5(4(4(1(3(2(3(1(4(5(2(2(5(x1)))))))))))))))) 0(2(3(5(3(4(1(1(4(3(0(2(1(0(5(5(4(x1))))))))))))))))) -> 0(5(4(5(4(3(5(1(0(0(5(5(0(0(1(4(x1)))))))))))))))) 4(4(2(2(1(1(1(1(2(3(0(3(5(1(4(1(3(x1))))))))))))))))) -> 4(5(2(0(3(3(2(1(1(3(0(0(5(3(3(3(x1)))))))))))))))) 0(3(1(3(5(4(3(4(2(4(1(3(0(3(4(5(5(2(3(x1))))))))))))))))))) -> 0(3(2(4(3(3(4(4(5(5(3(3(1(2(4(2(2(0(x1)))))))))))))))))) 3(3(0(1(0(4(1(4(2(1(0(5(3(3(2(1(3(5(0(x1))))))))))))))))))) -> 2(3(0(2(1(3(4(5(1(5(3(4(1(0(4(4(2(5(x1)))))))))))))))))) 1(3(3(5(4(3(5(2(4(3(3(5(0(0(1(3(5(3(4(5(x1)))))))))))))))))))) -> 3(0(4(3(1(5(3(3(5(2(1(0(5(0(1(1(1(5(0(3(5(x1))))))))))))))))))))) 2(0(5(1(5(0(1(0(4(4(5(2(4(2(5(3(4(3(0(5(x1)))))))))))))))))))) -> 2(3(2(2(1(5(4(0(0(2(3(4(0(1(4(4(2(5(5(x1))))))))))))))))))) 3(0(4(2(5(1(5(3(3(2(4(3(0(0(5(1(0(5(4(3(x1)))))))))))))))))))) -> 3(2(1(4(2(0(4(2(4(4(2(5(1(3(3(4(3(4(0(x1))))))))))))))))))) 3(2(0(1(0(5(1(3(1(4(3(5(4(5(5(5(5(5(1(5(x1)))))))))))))))))))) -> 3(1(4(4(5(3(5(2(1(4(4(0(1(3(4(1(3(1(5(3(5(x1))))))))))))))))))))) 3(3(1(0(0(1(1(0(4(4(2(3(4(0(2(3(5(5(0(2(x1)))))))))))))))))))) -> 5(2(2(4(5(5(0(2(4(3(3(2(1(2(4(5(2(x1))))))))))))))))) 3(0(5(5(1(5(5(1(1(3(5(0(1(1(3(1(5(4(4(4(5(x1))))))))))))))))))))) -> 5(2(4(3(1(4(3(3(2(3(0(4(0(1(2(1(4(2(2(0(x1)))))))))))))))))))) Proof: Bounds Processor: bound: 1 enrichment: match automaton: final states: {321,305,286,269,252,232,217,201,187,172,158,145,133, 122,109,96,86,75,68,58,48,41,34,27,21,16,13,9,5,1} transitions: 01(345) -> 346* 01(350) -> 351* 21(343) -> 344* 21(348) -> 349* 00(326) -> 327* 00(106) -> 107* 00(190) -> 191* 00(59) -> 60* 00(261) -> 262* 00(78) -> 79* 00(229) -> 230* 00(186) -> 172* 00(142) -> 143* 00(97) -> 98* 00(174) -> 175* 00(82) -> 83* 00(85) -> 75* 00(293) -> 294* 00(240) -> 241* 00(35) -> 36* 00(280) -> 281* 00(139) -> 140* 00(173) -> 174* 00(324) -> 325* 00(32) -> 33* 00(216) -> 201* 00(256) -> 257* 00(238) -> 239* 00(53) -> 54* 00(100) -> 101* 00(87) -> 88* 00(218) -> 219* 00(6) -> 28* 00(84) -> 85* 00(17) -> 97* 00(3) -> 10* 00(178) -> 179* 00(138) -> 139* 00(37) -> 38* 00(26) -> 21* 00(233) -> 234* 00(8) -> 5* 00(4) -> 1* 00(25) -> 26* 00(107) -> 108* 00(189) -> 190* 00(24) -> 25* 00(55) -> 56* 00(79) -> 80* 00(314) -> 315* 00(260) -> 261* 00(98) -> 99* 00(146) -> 147* 00(197) -> 198* 00(90) -> 91* 00(117) -> 118* 00(156) -> 157* 00(123) -> 124* 00(250) -> 251* 00(177) -> 178* 00(157) -> 145* 00(2) -> 17* f60() -> 2* 10(141) -> 142* 10(203) -> 322* 10(57) -> 48* 10(283) -> 284* 10(204) -> 205* 10(223) -> 224* 10(219) -> 220* 10(332) -> 333* 10(289) -> 290* 10(17) -> 35* 10(102) -> 103* 10(33) -> 27* 10(134) -> 135* 10(115) -> 116* 10(323) -> 324* 10(161) -> 162* 10(149) -> 150* 10(292) -> 293* 10(264) -> 265* 10(296) -> 297* 10(287) -> 288* 10(44) -> 45* 10(255) -> 256* 10(143) -> 144* 10(30) -> 31* 10(83) -> 84* 10(151) -> 152* 10(49) -> 50* 10(241) -> 242* 10(38) -> 39* 10(192) -> 193* 10(308) -> 309* 10(165) -> 166* 10(6) -> 22* 10(237) -> 238* 10(50) -> 51* 10(91) -> 92* 10(97) -> 123* 10(118) -> 119* 10(227) -> 228* 10(193) -> 194* 10(273) -> 274* 10(18) -> 76* 10(247) -> 248* 10(65) -> 66* 10(77) -> 78* 10(99) -> 100* 10(236) -> 237* 10(59) -> 173* 10(179) -> 180* 10(31) -> 32* 10(235) -> 236* 10(64) -> 65* 10(303) -> 304* 50(168) -> 169* 50(243) -> 244* 50(73) -> 74* 50(2) -> 6* 50(188) -> 189* 50(111) -> 112* 50(315) -> 316* 50(233) -> 287* 50(199) -> 200* 50(300) -> 301* 50(76) -> 77* 50(180) -> 181* 50(45) -> 46* 50(126) -> 127* 50(131) -> 132* 50(183) -> 184* 50(18) -> 19* 50(185) -> 186* 50(175) -> 176* 50(95) -> 86* 50(176) -> 177* 50(274) -> 275* 50(224) -> 225* 50(3) -> 306* 50(298) -> 299* 50(14) -> 15* 50(159) -> 160* 50(155) -> 156* 50(89) -> 90* 50(316) -> 317* 50(20) -> 16* 50(39) -> 40* 50(234) -> 235* 50(239) -> 240* 50(207) -> 208* 50(6) -> 14* 50(56) -> 57* 50(128) -> 129* 50(36) -> 37* 50(60) -> 61* 50(69) -> 70* 50(129) -> 130* 50(320) -> 305* 50(222) -> 223* 50(263) -> 264* 50(208) -> 209* 50(336) -> 321* 50(120) -> 121* 50(135) -> 136* 50(47) -> 41* 50(132) -> 122* 50(246) -> 247* 50(101) -> 102* 50(108) -> 96* 40(254) -> 255* 40(290) -> 291* 40(302) -> 303* 40(2) -> 59* 40(17) -> 110* 40(317) -> 318* 40(325) -> 326* 40(253) -> 254* 40(72) -> 73* 40(334) -> 335* 40(184) -> 185* 40(104) -> 105* 40(276) -> 277* 40(249) -> 250* 40(3) -> 4* 40(87) -> 218* 40(331) -> 332* 40(282) -> 283* 40(88) -> 89* 40(312) -> 313* 40(209) -> 210* 40(202) -> 203* 40(294) -> 295* 40(110) -> 111* 40(213) -> 214* 40(257) -> 258* 40(277) -> 278* 40(220) -> 221* 40(167) -> 168* 40(11) -> 12* 40(105) -> 106* 40(112) -> 113* 40(262) -> 263* 40(210) -> 211* 40(136) -> 137* 40(7) -> 87* 40(169) -> 170* 40(166) -> 167* 40(19) -> 20* 40(160) -> 161* 40(144) -> 133* 40(270) -> 271* 40(279) -> 280* 40(42) -> 43* 40(306) -> 307* 40(301) -> 302* 40(200) -> 187* 40(170) -> 171* 40(70) -> 71* 40(225) -> 226* 40(137) -> 138* 40(124) -> 125* 40(182) -> 183* 40(295) -> 296* 30(7) -> 8* 30(272) -> 273* 30(215) -> 216* 30(288) -> 289* 30(196) -> 197* 30(94) -> 95* 30(248) -> 249* 30(127) -> 128* 30(29) -> 30* 30(3) -> 146* 30(130) -> 131* 30(226) -> 227* 30(271) -> 272* 30(327) -> 328* 30(49) -> 188* 30(206) -> 207* 30(330) -> 331* 30(221) -> 222* 30(67) -> 58* 30(285) -> 269* 30(299) -> 300* 30(244) -> 245* 30(304) -> 286* 30(116) -> 117* 30(63) -> 64* 30(148) -> 149* 30(154) -> 155* 30(212) -> 213* 30(23) -> 24* 30(195) -> 196* 30(251) -> 232* 30(181) -> 182* 30(92) -> 93* 30(230) -> 231* 30(333) -> 334* 30(191) -> 192* 30(329) -> 330* 30(61) -> 62* 30(258) -> 259* 30(150) -> 151* 30(267) -> 268* 30(164) -> 165* 30(245) -> 246* 30(140) -> 141* 30(80) -> 81* 30(46) -> 47* 30(291) -> 292* 30(28) -> 69* 30(42) -> 49* 30(162) -> 163* 30(310) -> 311* 30(110) -> 270* 30(211) -> 212* 30(71) -> 72* 30(205) -> 206* 30(113) -> 114* 30(152) -> 153* 30(311) -> 312* 30(6) -> 233* 30(74) -> 68* 30(2) -> 42* 20(153) -> 154* 20(297) -> 298* 20(12) -> 9* 20(103) -> 104* 20(54) -> 55* 20(194) -> 195* 20(17) -> 18* 20(266) -> 267* 20(147) -> 148* 20(242) -> 243* 20(2) -> 3* 20(22) -> 23* 20(40) -> 34* 20(259) -> 260* 20(163) -> 164* 20(43) -> 44* 20(265) -> 266* 20(14) -> 253* 20(28) -> 29* 20(4) -> 134* 20(309) -> 310* 20(318) -> 319* 20(10) -> 11* 20(81) -> 82* 20(281) -> 282* 20(214) -> 215* 20(171) -> 158* 20(15) -> 13* 20(322) -> 323* 20(284) -> 285* 20(62) -> 63* 20(119) -> 120* 20(6) -> 7* 20(198) -> 199* 20(18) -> 202* 20(114) -> 115* 20(328) -> 329* 20(228) -> 229* 20(52) -> 53* 20(268) -> 252* 20(93) -> 94* 20(275) -> 276* 20(313) -> 314* 20(121) -> 109* 20(307) -> 308* 20(231) -> 217* 20(66) -> 67* 20(319) -> 320* 20(125) -> 126* 20(335) -> 336* 20(7) -> 159* 20(278) -> 279* 20(203) -> 204* 20(51) -> 52* 51(342) -> 343* 51(347) -> 348* 31(349) -> 350* 31(344) -> 345* 321 -> 42,69 351 -> 18,342,11 68 -> 35* 158 -> 17,10 217 -> 42,49 16 -> 6* 252 -> 3,18,29 232 -> 50* 75 -> 17* 109 -> 22* 172 -> 17,10 346 -> 29* 21 -> 17* 201 -> 17* 58 -> 3* 269 -> 42* 86 -> 3,7 183 -> 347* 13 -> 42,233 305 -> 42,49 1 -> 17* 34 -> 3,18,11 5 -> 3,18,29 187 -> 59* 41 -> 42,233 18 -> 342* 133 -> 42* 122 -> 42,146 145 -> 3,18 96 -> 42,49 286 -> 42,146 problem: Qed