YES Problem: 1(1(5(5(x1)))) -> 2(2(0(2(1(3(0(3(0(4(x1)))))))))) 3(2(2(4(x1)))) -> 4(2(0(2(0(4(1(3(2(0(x1)))))))))) 4(0(1(0(x1)))) -> 2(2(5(4(0(2(0(0(2(5(x1)))))))))) 4(0(1(0(x1)))) -> 3(5(2(2(2(5(1(0(2(5(x1)))))))))) 4(5(1(1(x1)))) -> 4(5(2(0(3(2(5(3(4(1(x1)))))))))) 0(0(2(4(1(x1))))) -> 3(5(0(1(4(0(3(0(4(1(x1)))))))))) 0(1(1(5(1(x1))))) -> 4(0(2(2(2(5(2(4(2(5(x1)))))))))) 1(3(4(2(4(x1))))) -> 1(4(2(0(3(4(0(2(5(1(x1)))))))))) 3(1(2(4(1(x1))))) -> 4(2(2(1(4(2(0(3(5(3(x1)))))))))) 0(0(2(4(0(1(x1)))))) -> 2(2(1(2(2(3(1(2(5(1(x1)))))))))) 0(5(1(2(4(5(x1)))))) -> 0(4(3(2(5(2(3(2(2(5(x1)))))))))) 0(5(4(2(4(5(x1)))))) -> 3(1(5(3(0(3(5(2(5(3(x1)))))))))) 1(4(4(1(1(5(x1)))))) -> 0(2(1(3(3(2(1(3(5(4(x1)))))))))) 1(5(0(1(5(5(x1)))))) -> 2(5(5(3(4(3(2(0(3(4(x1)))))))))) 1(5(2(4(1(0(x1)))))) -> 0(3(4(4(0(4(1(2(3(4(x1)))))))))) 2(3(4(2(3(1(x1)))))) -> 2(2(2(5(5(2(0(0(5(4(x1)))))))))) 2(4(2(4(5(2(x1)))))) -> 0(3(2(5(3(2(3(5(3(2(x1)))))))))) 2(5(0(1(1(5(x1)))))) -> 2(0(4(1(5(4(4(2(5(3(x1)))))))))) 4(0(0(1(1(0(x1)))))) -> 4(2(3(3(0(2(2(5(4(5(x1)))))))))) 4(0(1(1(5(2(x1)))))) -> 2(2(1(1(2(5(1(2(1(3(x1)))))))))) 4(1(1(4(5(1(x1)))))) -> 3(3(2(5(1(4(3(2(3(0(x1)))))))))) 4(2(4(4(5(0(x1)))))) -> 3(3(5(1(2(2(5(1(0(0(x1)))))))))) 4(5(2(3(4(1(x1)))))) -> 3(0(3(4(3(3(2(5(3(0(x1)))))))))) 4(5(2(4(2(4(x1)))))) -> 2(0(4(4(3(1(2(2(5(5(x1)))))))))) 5(5(3(0(0(3(x1)))))) -> 5(5(2(2(2(5(2(0(0(3(x1)))))))))) 0(1(1(0(5(5(0(x1))))))) -> 0(0(3(3(2(2(1(4(2(0(x1)))))))))) 0(3(1(2(3(3(1(x1))))))) -> 2(5(0(3(0(3(4(5(3(1(x1)))))))))) 0(4(0(0(4(2(1(x1))))))) -> 2(3(0(0(0(1(2(5(2(5(x1)))))))))) 0(4(2(4(5(1(1(x1))))))) -> 2(5(5(2(1(3(3(3(0(1(x1)))))))))) 1(1(1(1(4(0(4(x1))))))) -> 5(2(5(4(1(5(0(2(0(4(x1)))))))))) 1(1(1(1(4(5(5(x1))))))) -> 5(0(5(2(2(5(0(0(5(5(x1)))))))))) 1(1(1(5(4(3(0(x1))))))) -> 1(2(5(5(2(0(0(1(3(0(x1)))))))))) 1(1(3(5(4(0(1(x1))))))) -> 1(0(2(3(5(0(2(2(5(0(x1)))))))))) 1(1(4(2(4(4(5(x1))))))) -> 1(4(4(1(3(5(1(1(2(5(x1)))))))))) 1(2(0(1(5(0(1(x1))))))) -> 0(3(0(4(0(4(1(4(3(0(x1)))))))))) 1(3(1(3(1(5(0(x1))))))) -> 1(1(3(2(5(2(2(3(2(5(x1)))))))))) 1(5(3(5(4(4(2(x1))))))) -> 2(5(3(2(5(3(1(0(1(3(x1)))))))))) 2(0(1(1(1(2(1(x1))))))) -> 2(2(0(4(3(1(2(2(5(5(x1)))))))))) 2(1(2(4(1(2(4(x1))))))) -> 2(5(0(1(5(5(2(5(1(1(x1)))))))))) 2(3(4(1(1(5(3(x1))))))) -> 1(4(4(5(2(2(5(1(5(3(x1)))))))))) 2(4(1(0(4(3(2(x1))))))) -> 0(3(5(2(0(5(3(2(0(3(x1)))))))))) 3(4(1(0(4(2(1(x1))))))) -> 1(3(5(5(3(3(2(5(2(1(x1)))))))))) 3(4(2(4(0(0(4(x1))))))) -> 4(4(4(2(2(0(3(0(5(5(x1)))))))))) 3(4(2(4(3(5(3(x1))))))) -> 1(3(4(1(0(2(2(2(5(3(x1)))))))))) 4(1(5(3(4(1(5(x1))))))) -> 4(1(2(3(4(3(3(5(2(5(x1)))))))))) 4(2(2(4(5(4(2(x1))))))) -> 3(1(0(1(4(1(2(5(3(3(x1)))))))))) 4(2(4(5(5(5(0(x1))))))) -> 4(4(1(3(0(2(5(4(2(0(x1)))))))))) 4(4(3(1(2(3(1(x1))))))) -> 3(3(0(5(2(0(0(2(5(4(x1)))))))))) 4(5(4(2(1(2(4(x1))))))) -> 3(4(3(4(3(0(0(1(3(0(x1)))))))))) 5(1(2(3(2(4(5(x1))))))) -> 5(5(2(2(2(1(5(4(4(4(x1)))))))))) 5(4(0(0(2(3(4(x1))))))) -> 2(5(3(1(5(0(4(0(3(4(x1)))))))))) 5(4(4(1(2(4(5(x1))))))) -> 2(1(5(3(2(1(5(0(3(5(x1)))))))))) Proof: Bounds Processor: bound: 0 enrichment: match automaton: final states: {422,415,406,401,393,386,377,370,363,356,347,339,331, 322,319,311,303,295,287,278,270,262,254,245,237,228, 220,211,202,194,185,176,167,158,151,141,133,125,116, 107,99,91,84,74,65,57,49,39,32,22,12,1} transitions: 40(258) -> 259* 40(2) -> 3* 40(337) -> 338* 40(127) -> 128* 40(68) -> 69* 40(23) -> 159* 40(130) -> 131* 40(64) -> 57* 40(361) -> 362* 40(24) -> 58* 40(79) -> 80* 40(367) -> 368* 40(179) -> 180* 40(392) -> 386* 40(292) -> 293* 40(381) -> 382* 40(3) -> 407* 40(48) -> 39* 40(16) -> 17* 40(40) -> 41* 40(14) -> 221* 40(52) -> 53* 40(72) -> 73* 40(83) -> 74* 40(155) -> 156* 40(166) -> 158* 40(118) -> 416* 40(376) -> 370* 40(207) -> 208* 40(360) -> 361* 40(402) -> 403* 40(28) -> 29* 40(198) -> 199* 40(297) -> 298* 40(407) -> 408* 40(152) -> 153* 40(129) -> 130* 40(230) -> 231* 40(208) -> 209* 40(362) -> 356* 40(391) -> 392* 40(177) -> 296* 40(372) -> 373* 40(293) -> 294* 40(336) -> 337* 40(120) -> 121* 40(97) -> 98* 40(100) -> 152* 40(404) -> 405* 40(21) -> 12* 40(299) -> 300* 20(171) -> 172* 20(182) -> 183* 20(168) -> 169* 20(265) -> 266* 20(160) -> 161* 20(273) -> 274* 20(148) -> 149* 20(279) -> 280* 20(13) -> 14* 20(145) -> 146* 20(210) -> 202* 20(58) -> 59* 20(31) -> 22* 20(188) -> 189* 20(253) -> 245* 20(266) -> 267* 20(78) -> 79* 20(34) -> 35* 20(343) -> 344* 20(349) -> 350* 20(108) -> 394* 20(212) -> 340* 20(60) -> 61* 20(321) -> 319* 20(396) -> 397* 20(412) -> 413* 20(276) -> 277* 20(174) -> 175* 20(40) -> 348* 20(333) -> 334* 20(426) -> 427* 20(82) -> 83* 20(20) -> 21* 20(195) -> 196* 20(93) -> 94* 20(35) -> 36* 20(165) -> 166* 20(374) -> 375* 20(307) -> 308* 20(280) -> 281* 20(305) -> 306* 20(139) -> 140* 20(161) -> 162* 20(421) -> 415* 20(387) -> 388* 20(324) -> 325* 20(81) -> 82* 20(379) -> 380* 20(216) -> 217* 20(23) -> 24* 20(62) -> 63* 20(304) -> 305* 20(140) -> 133* 20(320) -> 321* 20(238) -> 239* 20(203) -> 204* 20(66) -> 67* 20(100) -> 364* 20(118) -> 119* 20(87) -> 88* 20(135) -> 136* 20(86) -> 87* 20(11) -> 1* 20(284) -> 285* 20(223) -> 224* 20(315) -> 316* 20(89) -> 90* 20(244) -> 237* 20(138) -> 139* 20(76) -> 100* 20(222) -> 223* 20(236) -> 228* 20(26) -> 27* 20(334) -> 335* 20(61) -> 62* 20(124) -> 116* 20(8) -> 9* 20(4) -> 255* 20(43) -> 44* 20(217) -> 218* 20(71) -> 72* 20(189) -> 190* 20(24) -> 92* 20(215) -> 216* 20(36) -> 37* 20(411) -> 412* 20(30) -> 31* 20(95) -> 96* 20(260) -> 261* 20(213) -> 214* 20(364) -> 365* 20(110) -> 111* 20(359) -> 360* 20(175) -> 167* 20(10) -> 11* 20(204) -> 205* 20(90) -> 84* 20(430) -> 422* 20(117) -> 126* 20(358) -> 359* 20(46) -> 47* 20(250) -> 251* 20(177) -> 178* 20(318) -> 311* 20(330) -> 322* 20(114) -> 115* 20(18) -> 19* 20(410) -> 411* 20(157) -> 151* 20(2) -> 142* 30(40) -> 229* 30(246) -> 247* 30(196) -> 197* 30(419) -> 420* 30(149) -> 150* 30(96) -> 97* 30(101) -> 102* 30(368) -> 369* 30(301) -> 302* 30(248) -> 249* 30(75) -> 378* 30(3) -> 117* 30(146) -> 147* 30(178) -> 179* 30(206) -> 207* 30(121) -> 122* 30(142) -> 143* 30(38) -> 32* 30(385) -> 377* 30(69) -> 70* 30(313) -> 314* 30(184) -> 176* 30(197) -> 198* 30(131) -> 132* 30(351) -> 352* 30(13) -> 177* 30(273) -> 402* 30(350) -> 351* 30(56) -> 49* 30(23) -> 423* 30(163) -> 164* 30(14) -> 15* 30(183) -> 184* 30(238) -> 371* 30(290) -> 291* 30(405) -> 401* 30(403) -> 404* 30(92) -> 93* 30(108) -> 109* 30(400) -> 393* 30(399) -> 400* 30(199) -> 200* 30(106) -> 99* 30(308) -> 309* 30(316) -> 317* 30(164) -> 165* 30(85) -> 86* 30(427) -> 428* 30(345) -> 346* 30(233) -> 234* 30(243) -> 244* 30(119) -> 120* 30(76) -> 77* 30(224) -> 225* 30(283) -> 284* 30(112) -> 113* 30(371) -> 372* 30(144) -> 145* 30(24) -> 304* 30(4) -> 5* 30(263) -> 357* 30(192) -> 193* 30(50) -> 51* 30(103) -> 104* 30(247) -> 248* 30(389) -> 390* 30(44) -> 45* 30(193) -> 185* 30(201) -> 194* 30(354) -> 355* 30(225) -> 226* 30(340) -> 341* 30(6) -> 7* 30(373) -> 374* 30(231) -> 232* 30(2) -> 75* 30(111) -> 112* 30(41) -> 42* 10(291) -> 292* 10(172) -> 173* 10(294) -> 287* 10(154) -> 155* 10(277) -> 270* 10(257) -> 258* 10(375) -> 376* 10(2) -> 40* 10(40) -> 323* 10(327) -> 328* 10(338) -> 331* 10(309) -> 310* 10(88) -> 89* 10(205) -> 206* 10(76) -> 332* 10(126) -> 127* 10(15) -> 16* 10(418) -> 419* 10(390) -> 391* 10(177) -> 271* 10(75) -> 168* 10(109) -> 110* 10(382) -> 383* 10(249) -> 250* 10(384) -> 385* 10(113) -> 114* 10(296) -> 297* 10(288) -> 289* 10(409) -> 410* 10(286) -> 278* 10(80) -> 81* 10(24) -> 288* 10(312) -> 313* 10(366) -> 367* 10(186) -> 187* 10(25) -> 33* 10(7) -> 8* 10(425) -> 426* 10(105) -> 106* 10(380) -> 381* 10(73) -> 65* 10(310) -> 303* 10(169) -> 170* 10(173) -> 174* 10(53) -> 54* 10(180) -> 181* 10(67) -> 85* 10(429) -> 430* 10(190) -> 191* 10(369) -> 363* 10(239) -> 240* 10(355) -> 347* 10(221) -> 222* 00(240) -> 241* 00(24) -> 25* 00(302) -> 295* 00(2) -> 13* 00(17) -> 18* 00(67) -> 68* 00(5) -> 6* 00(117) -> 118* 00(13) -> 186* 00(115) -> 107* 00(328) -> 329* 00(27) -> 28* 00(102) -> 103* 00(300) -> 301* 00(162) -> 163* 00(208) -> 320* 00(128) -> 129* 00(388) -> 389* 00(54) -> 55* 00(232) -> 233* 00(285) -> 286* 00(25) -> 26* 00(9) -> 10* 00(255) -> 256* 00(416) -> 417* 00(234) -> 235* 00(40) -> 246* 00(271) -> 272* 00(3) -> 4* 00(398) -> 399* 00(75) -> 212* 00(268) -> 269* 00(263) -> 264* 00(209) -> 210* 00(242) -> 243* 00(395) -> 396* 00(77) -> 78* 00(342) -> 343* 00(134) -> 135* 00(203) -> 263* 00(168) -> 312* 00(365) -> 366* 00(423) -> 424* 00(132) -> 125* 00(45) -> 46* 00(383) -> 384* 00(51) -> 52* 00(281) -> 282* 00(357) -> 358* 00(394) -> 395* 00(156) -> 157* 00(212) -> 213* 00(108) -> 134* 00(19) -> 20* 00(63) -> 64* 00(41) -> 50* 00(272) -> 273* 00(200) -> 201* 00(298) -> 299* 00(150) -> 141* 00(70) -> 71* 00(346) -> 339* 00(241) -> 242* 00(227) -> 220* 00(98) -> 91* 00(226) -> 227* 50(397) -> 398* 50(408) -> 409* 50(159) -> 160* 50(104) -> 105* 50(153) -> 154* 50(414) -> 406* 50(100) -> 101* 50(219) -> 211* 50(332) -> 333* 50(289) -> 290* 50(187) -> 188* 50(329) -> 330* 50(136) -> 137* 50(47) -> 48* 50(13) -> 279* 50(33) -> 34* 50(323) -> 324* 50(259) -> 260* 50(424) -> 425* 50(282) -> 283* 50(326) -> 327* 50(29) -> 30* 50(264) -> 265* 50(122) -> 123* 50(417) -> 418* 50(143) -> 144* 50(37) -> 38* 50(170) -> 171* 50(75) -> 76* 50(221) -> 387* 50(3) -> 108* 50(2) -> 23* 50(177) -> 195* 50(218) -> 219* 50(256) -> 257* 50(344) -> 345* 50(420) -> 421* 50(314) -> 315* 50(306) -> 307* 50(252) -> 253* 50(325) -> 326* 50(269) -> 262* 50(251) -> 252* 50(42) -> 43* 50(378) -> 379* 50(214) -> 215* 50(23) -> 203* 50(191) -> 192* 50(181) -> 182* 50(341) -> 342* 50(40) -> 66* 50(94) -> 95* 50(413) -> 414* 50(24) -> 238* 50(352) -> 353* 50(55) -> 56* 50(317) -> 318* 50(137) -> 138* 50(335) -> 336* 50(229) -> 230* 50(353) -> 354* 50(261) -> 254* 50(275) -> 276* 50(428) -> 429* 50(147) -> 148* 50(123) -> 124* 50(348) -> 349* 50(59) -> 60* 50(274) -> 275* 50(235) -> 236* 50(267) -> 268* f60() -> 2* 228 -> 13,212 415 -> 23,108 262 -> 40,323 151 -> 142,24,280 194 -> 3,159 422 -> 23,108 74 -> 75,229 254 -> 40,323 245 -> 13,4 393 -> 3,407 278 -> 40,323 158 -> 3* 295 -> 40* 370 -> 3,41 12 -> 75,143 270 -> 40,323 363 -> 75,117 237 -> 13,4 386 -> 3* 22 -> 3* 377 -> 3* 220 -> 13,246 116 -> 40* 311 -> 40,332 141 -> 142* 91 -> 13* 125 -> 40* 287 -> 40,323 1 -> 40,323 49 -> 13,186 107 -> 40* 99 -> 13,134 185 -> 3* 319 -> 142,14 65 -> 40,168 331 -> 142,126 347 -> 75,117,42 406 -> 23,66 57 -> 13,246 39 -> 3,159 133 -> 142,126 211 -> 23,203 167 -> 3* 84 -> 13,186 303 -> 40,168 401 -> 3,159 356 -> 75,117 202 -> 3,159 32 -> 3* 176 -> 3,41 322 -> 142,348 339 -> 142* problem: Qed