YES Problem: 0(0(1(x1))) -> 0(0(2(1(2(x1))))) 0(0(1(x1))) -> 0(0(3(1(4(x1))))) 0(1(0(x1))) -> 0(0(1(2(4(x1))))) 0(1(0(x1))) -> 2(1(2(0(0(x1))))) 0(1(0(x1))) -> 0(0(1(2(2(4(x1)))))) 0(1(0(x1))) -> 0(0(2(4(1(4(x1)))))) 0(4(0(x1))) -> 3(4(3(2(0(0(x1)))))) 0(0(1(0(x1)))) -> 0(0(0(1(4(x1))))) 0(0(4(1(x1)))) -> 0(0(2(1(4(x1))))) 0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1)))))) 0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1)))))) 0(1(3(0(x1)))) -> 0(0(3(1(4(x1))))) 0(1(3(0(x1)))) -> 0(3(0(1(2(x1))))) 0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1)))))) 0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1)))))) 0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1)))))) 0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1)))))) 0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1)))))) 0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1)))))) 0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1)))))) 0(3(1(0(x1)))) -> 0(0(3(1(4(x1))))) 0(4(0(1(x1)))) -> 0(0(2(1(4(x1))))) 0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1)))))) 0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1)))))) 0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1)))))) 0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1)))))) 0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1)))))) 0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1)))))) 0(5(1(0(x1)))) -> 0(0(5(1(2(x1))))) 3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1)))))) 3(5(1(0(x1)))) -> 0(5(1(3(2(x1))))) 3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1)))))) 3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1)))))) 3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1)))))) 0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1)))))) 0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1)))))) 0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1)))))) 0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1)))))) 0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1)))))) 0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1)))))) 0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1)))))) 0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1)))))) 0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1)))))) 0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1)))))) 0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1)))))) 3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1)))))) 3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1)))))) 3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1)))))) 3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1)))))) Proof: Bounds Processor: bound: 1 enrichment: match automaton: final states: {181,176,172,170,165,161,156,153,148,145,141,137,132, 129,123,119,114,109,105,101,98,93,91,87,82,77,72,71, 68,64,59,57,51,48,44,38,35,32,29,25,21,16,12,7,1} transitions: 01(189) -> 190* 01(206) -> 207* 01(231) -> 232* 01(213) -> 214* 01(230) -> 231* 01(309) -> 310* 01(289) -> 290* 01(236) -> 237* 01(188) -> 189* 01(237) -> 238* 01(290) -> 291* 01(207) -> 208* 01(308) -> 309* 01(212) -> 213* 11(210) -> 211* 11(287) -> 288* 11(204) -> 205* 11(270) -> 271* 11(282) -> 283* 11(234) -> 235* 11(228) -> 229* 11(306) -> 307* 11(254) -> 255* 11(266) -> 267* 11(250) -> 251* 11(186) -> 187* 00(171) -> 170* 00(182) -> 183* 00(47) -> 44* 00(160) -> 156* 00(88) -> 89* 00(179) -> 180* 00(5) -> 6* 00(58) -> 57* 00(34) -> 32* 00(108) -> 105* 00(154) -> 155* 00(39) -> 157* 00(75) -> 76* 00(42) -> 43* 00(103) -> 104* 00(52) -> 115* 00(27) -> 28* 00(15) -> 12* 00(33) -> 34* 00(139) -> 140* 00(125) -> 126* 00(23) -> 24* 00(100) -> 98* 00(14) -> 15* 00(6) -> 1* 00(11) -> 7* 00(17) -> 18* 00(164) -> 161* 00(3) -> 78* 00(76) -> 72* 00(151) -> 152* 00(155) -> 153* 00(37) -> 35* 00(124) -> 125* 00(8) -> 94* 00(4) -> 49* 00(43) -> 38* 00(24) -> 21* 00(55) -> 56* 00(36) -> 37* 00(166) -> 167* 00(99) -> 100* 00(50) -> 48* 00(110) -> 111* 00(54) -> 69* 00(10) -> 11* 00(133) -> 134* 00(9) -> 33* 00(56) -> 51* 00(28) -> 25* 00(46) -> 47* 00(177) -> 178* 00(157) -> 173* 00(2) -> 17* f60() -> 2* 50(39) -> 110* 50(17) -> 60* 50(134) -> 135* 50(78) -> 79* 50(28) -> 71* 50(122) -> 119* 50(168) -> 169* 50(107) -> 108* 50(2) -> 52* 50(89) -> 92* 50(4) -> 99* 50(144) -> 141* 50(84) -> 85* 50(140) -> 137* 50(183) -> 184* 50(9) -> 88* 50(46) -> 171* 50(92) -> 91* 50(169) -> 165* 50(94) -> 162* 50(97) -> 93* 50(175) -> 172* 50(152) -> 148* 50(180) -> 176* 50(146) -> 147* 50(90) -> 87* 50(184) -> 181* 40(2) -> 8* 40(79) -> 80* 40(95) -> 96* 40(150) -> 151* 40(65) -> 66* 40(70) -> 68* 40(30) -> 31* 40(9) -> 26* 40(147) -> 145* 40(39) -> 40* 40(4) -> 45* 40(157) -> 158* 40(60) -> 61* 40(124) -> 149* 40(94) -> 95* 40(142) -> 143* 40(8) -> 177* 40(17) -> 83* 20(52) -> 53* 20(66) -> 67* 20(4) -> 5* 20(2) -> 3* 20(13) -> 22* 20(115) -> 116* 20(20) -> 16* 20(102) -> 103* 20(162) -> 163* 20(96) -> 97* 20(163) -> 164* 20(9) -> 36* 20(116) -> 117* 20(111) -> 112* 20(113) -> 109* 20(3) -> 73* 20(18) -> 19* 20(60) -> 65* 20(11) -> 58* 20(84) -> 146* 20(8) -> 13* 20(173) -> 174* 20(85) -> 86* 20(159) -> 160* 20(63) -> 59* 20(78) -> 120* 20(41) -> 42* 20(26) -> 27* 20(126) -> 127* 30(158) -> 159* 30(149) -> 150* 30(104) -> 101* 30(81) -> 77* 30(127) -> 128* 30(3) -> 106* 30(86) -> 82* 30(49) -> 50* 30(178) -> 179* 30(53) -> 54* 30(39) -> 133* 30(138) -> 139* 30(118) -> 114* 30(128) -> 123* 30(14) -> 154* 30(143) -> 144* 30(9) -> 10* 30(61) -> 130* 30(89) -> 90* 30(4) -> 182* 30(19) -> 30* 30(167) -> 168* 30(74) -> 75* 30(120) -> 121* 30(45) -> 46* 30(31) -> 29* 30(2) -> 39* 10(54) -> 55* 10(69) -> 70* 10(2) -> 124* 10(22) -> 23* 10(40) -> 41* 10(124) -> 166* 10(117) -> 118* 10(13) -> 14* 10(62) -> 63* 10(136) -> 132* 10(131) -> 129* 10(83) -> 84* 10(106) -> 107* 10(80) -> 81* 10(135) -> 136* 10(8) -> 9* 10(61) -> 62* 10(121) -> 122* 10(125) -> 142* 10(3) -> 4* 10(174) -> 175* 10(112) -> 113* 10(73) -> 74* 10(78) -> 138* 10(19) -> 20* 10(53) -> 102* 10(67) -> 64* 10(130) -> 131* 41(249) -> 250* 41(265) -> 266* 41(305) -> 306* 41(281) -> 282* 41(269) -> 270* 41(253) -> 254* 21(211) -> 212* 21(229) -> 230* 21(203) -> 204* 21(285) -> 286* 21(286) -> 287* 21(227) -> 228* 21(205) -> 206* 21(187) -> 188* 21(209) -> 210* 21(235) -> 236* 21(185) -> 186* 21(233) -> 234* 31(271) -> 272* 31(288) -> 289* 31(267) -> 268* 31(307) -> 308* 31(283) -> 284* 31(251) -> 252* 31(255) -> 256* 291 -> 48* 156 -> 17,94 238 -> 12* 132 -> 17,125 148 -> 17,125 68 -> 17,125 190 -> 34* 48 -> 17,125 256 -> 206* 35 -> 94,17,18 310 -> 140* 64 -> 94,17,125 137 -> 17,125 7 -> 157,125,17,18 77 -> 17,94 12 -> 17,125 93 -> 17,94 114 -> 39* 16 -> 17,125 252 -> 188* 284 -> 236* 232 -> 126* 2 -> 269,227 82 -> 17,94 105 -> 39* 22 -> 253,203 54 -> 265,209 109 -> 39* 153 -> 17,157 172 -> 39* 141 -> 17,125 72 -> 17,157 21 -> 17,125 268 -> 212* 161 -> 17,94 208 -> 21* 170 -> 39* 91 -> 17,94 38 -> 17,18 44 -> 17,125 101 -> 39* 13 -> 281,233 165 -> 17,115 71 -> 17,125 8 -> 249,185 123 -> 17,125 1 -> 17,18 59 -> 17,125 57 -> 17,125,33 3 -> 305,285 145 -> 17,125 119 -> 39* 129 -> 17,125 181 -> 39* 51 -> 17,125 214 -> 51* 98 -> 17,115 87 -> 17,94 29 -> 17,94 32 -> 17,18,126 25 -> 17,125 176 -> 39* 272 -> 230* problem: Qed