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