YES Problem: 0(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 1(0(0(2(x1)))) -> 2(3(0(0(1(x1))))) 1(0(0(2(x1)))) -> 1(0(1(1(2(0(x1)))))) 1(0(0(2(x1)))) -> 1(3(3(0(2(0(x1)))))) 1(0(0(2(x1)))) -> 3(0(0(1(1(2(x1)))))) 1(0(2(2(x1)))) -> 2(1(2(3(0(x1))))) 1(0(2(2(x1)))) -> 1(1(1(2(2(0(x1)))))) 1(3(4(2(x1)))) -> 1(1(2(3(4(x1))))) 1(3(4(2(x1)))) -> 1(2(3(3(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(4(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(5(4(x1)))))) 1(3(5(2(x1)))) -> 2(3(1(0(5(x1))))) 1(3(5(2(x1)))) -> 4(5(1(2(3(x1))))) 3(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 3(4(0(2(x1)))) -> 3(0(0(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(1(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(5(2(4(x1))))) 3(4(0(2(x1)))) -> 3(1(0(2(4(x1))))) 3(4(0(2(x1)))) -> 4(1(2(3(0(x1))))) 3(4(0(2(x1)))) -> 2(0(4(3(3(0(x1)))))) 3(4(0(2(x1)))) -> 3(0(2(1(1(4(x1)))))) 3(4(0(2(x1)))) -> 3(3(0(5(2(4(x1)))))) 3(4(0(2(x1)))) -> 4(2(3(3(3(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(3(2(5(x1))))) 3(5(0(2(x1)))) -> 2(5(3(0(0(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(0(2(5(4(x1)))))) 3(5(0(2(x1)))) -> 5(5(2(3(0(3(x1)))))) 0(2(3(4(2(x1))))) -> 3(0(2(2(4(5(x1)))))) 0(3(4(0(2(x1))))) -> 0(3(1(0(4(2(x1)))))) 0(3(5(0(2(x1))))) -> 2(1(0(5(3(0(x1)))))) 1(0(0(4(2(x1))))) -> 0(4(5(1(0(2(x1)))))) 1(0(3(5(2(x1))))) -> 4(5(3(1(2(0(x1)))))) 1(1(0(2(2(x1))))) -> 1(1(2(0(1(2(x1)))))) 1(3(4(0(2(x1))))) -> 1(2(3(0(1(4(x1)))))) 1(3(5(0(2(x1))))) -> 1(0(2(5(2(3(x1)))))) 3(1(0(0(2(x1))))) -> 3(0(1(2(2(0(x1)))))) 3(1(3(5(2(x1))))) -> 3(0(3(5(1(2(x1)))))) 3(3(4(0(2(x1))))) -> 3(0(0(4(2(3(x1)))))) 3(4(0(0(2(x1))))) -> 3(0(0(4(4(2(x1)))))) 3(4(1(0(2(x1))))) -> 3(1(2(3(0(4(x1)))))) 3(4(1(5(2(x1))))) -> 2(3(0(1(4(5(x1)))))) 3(4(2(0(2(x1))))) -> 3(2(0(4(2(3(x1)))))) 3(4(2(0(2(x1))))) -> 4(2(2(3(0(3(x1)))))) 3(5(0(0(2(x1))))) -> 0(3(0(2(4(5(x1)))))) 3(5(0(4(2(x1))))) -> 2(0(4(4(5(3(x1)))))) 3(5(0(4(2(x1))))) -> 2(5(4(3(0(0(x1)))))) 3(5(3(4(2(x1))))) -> 0(5(4(2(3(3(x1)))))) Proof: String Reversal Processor: 2(0(1(0(x1)))) -> 0(2(1(0(3(x1))))) 2(0(0(1(x1)))) -> 1(0(0(3(2(x1))))) 2(0(0(1(x1)))) -> 0(2(1(1(0(1(x1)))))) 2(0(0(1(x1)))) -> 0(2(0(3(3(1(x1)))))) 2(0(0(1(x1)))) -> 2(1(1(0(0(3(x1)))))) 2(2(0(1(x1)))) -> 0(3(2(1(2(x1))))) 2(2(0(1(x1)))) -> 0(2(2(1(1(1(x1)))))) 2(4(3(1(x1)))) -> 4(3(2(1(1(x1))))) 2(4(3(1(x1)))) -> 5(4(3(3(2(1(x1)))))) 2(4(3(1(x1)))) -> 4(4(4(3(2(1(x1)))))) 2(4(3(1(x1)))) -> 5(4(4(3(2(1(x1)))))) 2(4(3(1(x1)))) -> 5(4(5(3(2(1(x1)))))) 2(4(3(1(x1)))) -> 4(5(5(3(2(1(x1)))))) 2(5(3(1(x1)))) -> 5(0(1(3(2(x1))))) 2(5(3(1(x1)))) -> 3(2(1(5(4(x1))))) 2(0(1(3(x1)))) -> 0(2(1(0(3(x1))))) 2(0(4(3(x1)))) -> 4(2(0(0(3(x1))))) 2(0(4(3(x1)))) -> 4(2(1(0(3(x1))))) 2(0(4(3(x1)))) -> 4(2(5(0(3(x1))))) 2(0(4(3(x1)))) -> 4(2(0(1(3(x1))))) 2(0(4(3(x1)))) -> 0(3(2(1(4(x1))))) 2(0(4(3(x1)))) -> 0(3(3(4(0(2(x1)))))) 2(0(4(3(x1)))) -> 4(1(1(2(0(3(x1)))))) 2(0(4(3(x1)))) -> 4(2(5(0(3(3(x1)))))) 2(0(4(3(x1)))) -> 0(3(3(3(2(4(x1)))))) 2(0(5(3(x1)))) -> 5(2(3(0(3(x1))))) 2(0(5(3(x1)))) -> 0(0(0(3(5(2(x1)))))) 2(0(5(3(x1)))) -> 4(5(2(0(0(3(x1)))))) 2(0(5(3(x1)))) -> 3(0(3(2(5(5(x1)))))) 2(4(3(2(0(x1))))) -> 5(4(2(2(0(3(x1)))))) 2(0(4(3(0(x1))))) -> 2(4(0(1(3(0(x1)))))) 2(0(5(3(0(x1))))) -> 0(3(5(0(1(2(x1)))))) 2(4(0(0(1(x1))))) -> 2(0(1(5(4(0(x1)))))) 2(5(3(0(1(x1))))) -> 0(2(1(3(5(4(x1)))))) 2(2(0(1(1(x1))))) -> 2(1(0(2(1(1(x1)))))) 2(0(4(3(1(x1))))) -> 4(1(0(3(2(1(x1)))))) 2(0(5(3(1(x1))))) -> 3(2(5(2(0(1(x1)))))) 2(0(0(1(3(x1))))) -> 0(2(2(1(0(3(x1)))))) 2(5(3(1(3(x1))))) -> 2(1(5(3(0(3(x1)))))) 2(0(4(3(3(x1))))) -> 3(2(4(0(0(3(x1)))))) 2(0(0(4(3(x1))))) -> 2(4(4(0(0(3(x1)))))) 2(0(1(4(3(x1))))) -> 4(0(3(2(1(3(x1)))))) 2(5(1(4(3(x1))))) -> 5(4(1(0(3(2(x1)))))) 2(0(2(4(3(x1))))) -> 3(2(4(0(2(3(x1)))))) 2(0(2(4(3(x1))))) -> 3(0(3(2(2(4(x1)))))) 2(0(0(5(3(x1))))) -> 5(4(2(0(3(0(x1)))))) 2(4(0(5(3(x1))))) -> 3(5(4(4(0(2(x1)))))) 2(4(0(5(3(x1))))) -> 0(0(3(4(5(2(x1)))))) 2(4(3(5(3(x1))))) -> 3(3(2(4(5(0(x1)))))) Bounds Processor: bound: 1 enrichment: match automaton: final states: {179,175,172,168,164,159,156,152,150,147,144,142,138, 135,132,128,123,119,113,110,104,102,97,94,89,84,80, 75,71,67,64,63,61,56,53,51,48,47,44,39,36,31,27,23, 18,12,7,1} transitions: 40(2) -> 57* 40(111) -> 112* 40(38) -> 36* 40(76) -> 77* 40(77) -> 173* 40(180) -> 181* 40(45) -> 46* 40(24) -> 148* 40(114) -> 124* 40(137) -> 135* 40(62) -> 61* 40(70) -> 67* 40(103) -> 102* 40(52) -> 51* 40(49) -> 50* 40(83) -> 80* 40(155) -> 152* 40(161) -> 162* 40(41) -> 45* 40(148) -> 151* 40(6) -> 63* 40(157) -> 158* 40(66) -> 64* 40(117) -> 118* 40(98) -> 176* 40(88) -> 84* 40(46) -> 44* 40(42) -> 43* 40(170) -> 171* 11(192) -> 193* 11(197) -> 198* 11(215) -> 216* 11(216) -> 217* 11(214) -> 215* 21(193) -> 194* 21(217) -> 218* 21(198) -> 199* 21(218) -> 219* 21(196) -> 197* 00(122) -> 119* 00(116) -> 117* 00(160) -> 161* 00(115) -> 169* 00(68) -> 69* 00(13) -> 14* 00(41) -> 136* 00(108) -> 109* 00(154) -> 155* 00(143) -> 142* 00(126) -> 127* 00(20) -> 21* 00(85) -> 86* 00(22) -> 18* 00(101) -> 97* 00(93) -> 89* 00(35) -> 31* 00(100) -> 101* 00(6) -> 1* 00(17) -> 12* 00(3) -> 4* 00(178) -> 175* 00(74) -> 71* 00(37) -> 133* 00(8) -> 76* 00(4) -> 24* 00(131) -> 128* 00(30) -> 27* 00(166) -> 167* 00(79) -> 75* 00(99) -> 100* 00(54) -> 55* 00(10) -> 11* 00(9) -> 10* 00(28) -> 120* 00(177) -> 178* 00(2) -> 114* 30(153) -> 154* 30(40) -> 41* 30(149) -> 147* 30(29) -> 30* 30(3) -> 85* 30(121) -> 122* 30(90) -> 91* 30(182) -> 183* 30(107) -> 108* 30(13) -> 19* 30(163) -> 159* 30(183) -> 179* 30(92) -> 93* 30(141) -> 138* 30(176) -> 177* 30(60) -> 56* 30(114) -> 115* 30(91) -> 92* 30(8) -> 9* 30(165) -> 166* 30(174) -> 172* 30(77) -> 78* 30(4) -> 95* 30(37) -> 38* 30(98) -> 99* 30(19) -> 20* 30(58) -> 129* 30(167) -> 164* 30(78) -> 79* 30(2) -> 3* 30(109) -> 104* 30(41) -> 42* 30(73) -> 74* 01(200) -> 201* 01(191) -> 192* 01(194) -> 195* 10(57) -> 72* 10(2) -> 13* 10(14) -> 15* 10(4) -> 5* 10(10) -> 157* 10(81) -> 82* 10(13) -> 32* 10(15) -> 16* 10(136) -> 137* 10(145) -> 146* 10(82) -> 83* 10(9) -> 54* 10(133) -> 134* 10(8) -> 28* 10(24) -> 25* 10(58) -> 59* 10(32) -> 33* 10(125) -> 126* 10(129) -> 130* 10(25) -> 26* 10(3) -> 68* 10(11) -> 7* 10(115) -> 116* 20(16) -> 17* 20(68) -> 153* 20(24) -> 62* 20(4) -> 81* 20(2) -> 8* 20(5) -> 6* 20(181) -> 182* 20(21) -> 22* 20(13) -> 40* 20(127) -> 123* 20(72) -> 73* 20(162) -> 163* 20(146) -> 144* 20(57) -> 90* 20(140) -> 141* 20(69) -> 70* 20(3) -> 160* 20(28) -> 29* 20(87) -> 88* 20(90) -> 165* 20(134) -> 132* 20(6) -> 143* 20(95) -> 96* 20(32) -> 37* 20(34) -> 35* 20(130) -> 131* 20(169) -> 170* 20(118) -> 113* 20(59) -> 60* 20(14) -> 139* 20(26) -> 23* 20(81) -> 111* 20(148) -> 149* 20(151) -> 150* 20(33) -> 34* 20(65) -> 66* 20(106) -> 107* 31(190) -> 191* 31(199) -> 200* 50(112) -> 110* 50(57) -> 58* 50(86) -> 87* 50(158) -> 156* 50(8) -> 98* 50(124) -> 125* 50(41) -> 49* 50(2) -> 105* 50(43) -> 39* 50(171) -> 168* 50(49) -> 52* 50(4) -> 65* 50(62) -> 103* 50(50) -> 48* 50(114) -> 180* 50(173) -> 174* 50(46) -> 47* 50(120) -> 121* 50(139) -> 140* 50(95) -> 145* 50(55) -> 53* 50(96) -> 94* 50(105) -> 106* f60() -> 2* 156 -> 8* 94 -> 8* 56 -> 8* 27 -> 8* 144 -> 8* 195 -> 70* 142 -> 8* 132 -> 8* 159 -> 8* 168 -> 8* 164 -> 8* 47 -> 8,90 48 -> 8,90 64 -> 8* 113 -> 8* 7 -> 8* 104 -> 8* 12 -> 8* 63 -> 8* 2 -> 190* 53 -> 8* 67 -> 8* 75 -> 8* 172 -> 8,90 150 -> 8* 138 -> 8* 201 -> 165* 36 -> 8,90 125 -> 214,196 179 -> 8,90 135 -> 8* 44 -> 8,90 71 -> 8* 123 -> 8,90 1 -> 8,139 31 -> 8* 175 -> 8,90 110 -> 8,90 147 -> 8* 219 -> 200* 39 -> 8,90 18 -> 8* 119 -> 8* 84 -> 8* 97 -> 8* 51 -> 8,90 152 -> 8,139 80 -> 8* 128 -> 8* 89 -> 8* 102 -> 8* 61 -> 8* 23 -> 8* problem: Qed