YES Problem: 0(0(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(x1)))))) Proof: String Reversal Processor: 0(0(x1)) -> 2(0(1(0(x1)))) 0(0(x1)) -> 0(2(0(1(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 0(2(1(0(1(x1))))) 0(0(x1)) -> 3(0(2(0(1(x1))))) 0(0(x1)) -> 0(2(2(0(1(x1))))) 0(0(x1)) -> 0(2(0(1(2(x1))))) 0(0(x1)) -> 2(1(2(0(1(0(x1)))))) 0(0(x1)) -> 2(2(0(1(0(1(x1)))))) 0(0(x1)) -> 1(0(3(1(0(1(x1)))))) 0(0(x1)) -> 2(0(1(4(0(1(x1)))))) 0(0(x1)) -> 0(2(0(1(1(1(x1)))))) 0(0(x1)) -> 2(2(0(4(0(3(x1)))))) 0(0(x1)) -> 4(0(1(0(1(3(x1)))))) 0(0(0(x1))) -> 4(0(4(0(1(0(x1)))))) 0(0(0(x1))) -> 2(0(1(0(0(3(x1)))))) 0(0(3(x1))) -> 3(0(2(0(3(x1))))) 0(0(3(x1))) -> 2(0(4(2(0(3(x1)))))) 0(2(5(x1))) -> 5(3(2(0(x1)))) 0(2(5(x1))) -> 2(0(5(3(x1)))) 0(2(5(x1))) -> 5(3(3(2(0(x1))))) 0(2(5(x1))) -> 5(3(2(0(1(x1))))) 0(2(5(x1))) -> 4(2(0(1(5(x1))))) 0(2(5(x1))) -> 2(2(2(1(0(5(x1)))))) 0(2(5(x1))) -> 2(0(1(5(3(5(x1)))))) 0(2(5(0(x1)))) -> 2(2(0(5(0(x1))))) 0(0(4(3(x1)))) -> 5(4(0(3(3(0(x1)))))) 0(0(4(3(x1)))) -> 0(3(5(4(0(3(x1)))))) 0(0(1(5(x1)))) -> 5(1(0(1(3(0(x1)))))) 0(4(1(5(x1)))) -> 4(2(5(1(0(x1))))) 0(5(1(5(x1)))) -> 5(3(0(1(5(x1))))) 0(2(2(5(x1)))) -> 5(4(2(1(2(0(x1)))))) 0(2(3(5(x1)))) -> 2(1(0(3(5(x1))))) 0(2(3(5(x1)))) -> 2(0(3(5(3(3(x1)))))) 0(0(4(5(x1)))) -> 2(0(5(5(4(0(x1)))))) 0(2(4(5(x1)))) -> 0(5(3(4(2(x1))))) 0(2(4(5(x1)))) -> 4(2(2(0(5(x1))))) 0(2(4(5(x1)))) -> 2(0(5(4(5(x1))))) 0(2(5(3(0(x1))))) -> 0(3(5(2(0(3(x1)))))) 0(2(5(3(3(x1))))) -> 2(0(3(2(5(3(x1)))))) 0(2(5(3(3(x1))))) -> 2(0(5(3(3(4(x1)))))) 0(2(5(0(5(x1))))) -> 2(0(5(5(3(0(x1)))))) 0(0(4(1(5(x1))))) -> 4(1(0(5(2(0(x1)))))) 0(2(3(3(5(x1))))) -> 2(0(3(3(2(5(x1)))))) 0(0(3(4(5(x1))))) -> 5(3(0(4(0(1(x1)))))) Bounds Processor: bound: 1 enrichment: match automaton: final states: {163,158,154,150,144,140,137,133,130,126,121,116,113, 109,107,104,100,97,92,88,83,78,73,71,69,66,63,60,57, 53,50,45,39,34,30,27,25,23,18,16,15,13,10,6,1} transitions: 21(206) -> 207* 21(214) -> 215* 21(196) -> 197* 21(169) -> 170* 21(183) -> 184* 21(204) -> 205* 41(222) -> 223* 41(248) -> 249* 41(232) -> 233* 41(256) -> 257* 20(153) -> 150* 20(115) -> 113* 20(68) -> 66* 20(5) -> 1* 20(44) -> 39* 20(41) -> 58* 20(162) -> 158* 20(143) -> 140* 20(12) -> 26* 20(120) -> 116* 20(82) -> 78* 20(33) -> 30* 20(81) -> 82* 20(125) -> 121* 20(62) -> 60* 20(136) -> 133* 20(87) -> 83* 20(11) -> 14* 20(3) -> 64* 20(74) -> 159* 20(76) -> 77* 20(37) -> 38* 20(26) -> 25* 20(21) -> 22* 20(8) -> 9* 20(43) -> 44* 20(131) -> 132* 20(24) -> 23* 20(80) -> 81* 20(79) -> 131* 20(67) -> 141* 20(110) -> 111* 20(105) -> 106* 20(90) -> 91* 20(9) -> 17* 20(91) -> 88* 20(56) -> 53* 20(149) -> 144* 20(2) -> 19* f60() -> 2* 50(112) -> 109* 50(134) -> 135* 50(108) -> 107* 50(58) -> 138* 50(103) -> 100* 50(122) -> 123* 50(3) -> 89* 50(2) -> 74* 50(151) -> 152* 50(4) -> 105* 50(117) -> 118* 50(84) -> 85* 50(165) -> 163* 50(42) -> 98* 50(40) -> 67* 50(128) -> 129* 50(72) -> 71* 50(65) -> 63* 50(96) -> 92* 50(93) -> 151* 50(147) -> 148* 50(123) -> 124* 50(70) -> 69* 50(64) -> 155* 40(2) -> 145* 40(111) -> 112* 40(77) -> 73* 40(95) -> 96* 40(74) -> 134* 40(3) -> 122* 40(52) -> 50* 40(49) -> 45* 40(41) -> 42* 40(157) -> 154* 40(5) -> 51* 40(58) -> 61* 40(8) -> 31* 40(132) -> 130* 40(106) -> 104* 40(19) -> 127* 00(89) -> 90* 00(22) -> 18* 00(4) -> 5* 00(2) -> 3* 00(17) -> 16* 00(119) -> 120* 00(67) -> 68* 00(48) -> 49* 00(31) -> 164* 00(74) -> 79* 00(135) -> 136* 00(20) -> 21* 00(61) -> 62* 00(94) -> 95* 00(161) -> 162* 00(101) -> 102* 00(9) -> 6* 00(139) -> 137* 00(40) -> 41* 00(28) -> 29* 00(36) -> 37* 00(75) -> 76* 00(46) -> 47* 00(129) -> 126* 00(55) -> 56* 00(155) -> 156* 00(152) -> 153* 00(38) -> 34* 00(99) -> 97* 00(32) -> 33* 00(11) -> 12* 00(84) -> 114* 00(51) -> 52* 00(58) -> 59* 00(7) -> 8* 00(142) -> 143* 00(86) -> 87* 00(14) -> 13* 00(41) -> 54* 00(42) -> 43* 00(148) -> 149* 00(124) -> 125* 30(65) -> 70* 30(40) -> 117* 30(127) -> 128* 30(3) -> 93* 30(146) -> 147* 30(145) -> 146* 30(138) -> 139* 30(118) -> 119* 30(64) -> 65* 30(93) -> 94* 30(9) -> 72* 30(11) -> 28* 30(141) -> 142* 30(164) -> 165* 30(76) -> 108* 30(59) -> 57* 30(98) -> 99* 30(6) -> 15* 30(74) -> 84* 30(160) -> 161* 30(159) -> 160* 30(2) -> 40* 10(12) -> 10* 10(54) -> 55* 10(156) -> 157* 10(1) -> 24* 10(85) -> 86* 10(2) -> 7* 10(40) -> 46* 10(47) -> 48* 10(102) -> 103* 10(79) -> 80* 10(64) -> 110* 10(114) -> 115* 10(29) -> 27* 10(8) -> 11* 10(93) -> 101* 10(7) -> 35* 10(3) -> 4* 10(19) -> 20* 10(35) -> 36* 10(74) -> 75* 10(31) -> 32* 31(198) -> 199* 31(250) -> 251* 31(230) -> 231* 31(220) -> 221* 11(244) -> 245* 11(167) -> 168* 11(186) -> 187* 11(181) -> 182* 11(212) -> 213* 11(188) -> 189* 11(246) -> 247* 11(228) -> 229* 01(182) -> 183* 01(245) -> 246* 01(184) -> 185* 01(168) -> 169* 01(166) -> 167* 01(231) -> 232* 01(187) -> 188* 01(247) -> 248* 163 -> 3,54 27 -> 3* 144 -> 3* 92 -> 3* 215 -> 169* 154 -> 3* 83 -> 3* 231 -> 244* 158 -> 3* 189 -> 54* 137 -> 3* 30 -> 3* 126 -> 3* 182 -> 228* 113 -> 3* 69 -> 3* 100 -> 3* 140 -> 3* 104 -> 3* 63 -> 3* 16 -> 3* 66 -> 3* 45 -> 3* 188 -> 214* 2 -> 250* 53 -> 3* 249 -> 54* 88 -> 3* 109 -> 3* 116 -> 3* 6 -> 3* 121 -> 3* 257 -> 168* 207 -> 181* 150 -> 3* 251 -> 182* 170 -> 212,54 233 -> 187* 73 -> 3* 197 -> 184* 60 -> 3* 183 -> 222,186 13 -> 3* 71 -> 3* 40 -> 230,206,181,166 1 -> 3* 107 -> 3,79 130 -> 3* 185 -> 198,54 199 -> 54* 34 -> 3* 187 -> 220,196 213 -> 169* 57 -> 3* 50 -> 3* 184 -> 256,204 39 -> 3* 18 -> 3* 133 -> 3* 15 -> 3* 97 -> 3* 10 -> 3* 229 -> 181* 205 -> 184* 25 -> 3* 221 -> 187* 23 -> 3* 223 -> 167* 78 -> 3* problem: Qed