YES Problem: 0(0(1(0(x1)))) -> 0(2(0(0(3(1(x1)))))) 0(0(1(0(x1)))) -> 0(2(0(4(1(0(x1)))))) 0(0(1(0(x1)))) -> 2(0(0(0(2(1(x1)))))) 3(0(1(0(x1)))) -> 0(2(3(1(0(x1))))) 3(0(1(0(x1)))) -> 3(1(0(0(2(x1))))) 3(0(1(0(x1)))) -> 3(1(1(0(0(x1))))) 3(0(1(0(x1)))) -> 3(1(2(0(0(x1))))) 3(0(1(0(x1)))) -> 3(1(5(0(0(x1))))) 3(0(1(0(x1)))) -> 3(5(1(0(0(x1))))) 3(0(1(0(x1)))) -> 5(0(3(1(0(x1))))) 3(0(1(0(x1)))) -> 2(0(2(3(1(0(x1)))))) 3(0(1(0(x1)))) -> 2(2(0(3(1(0(x1)))))) 3(0(1(0(x1)))) -> 3(1(5(0(0(0(x1)))))) 3(0(1(0(x1)))) -> 3(1(5(0(2(0(x1)))))) 3(0(1(0(x1)))) -> 3(1(5(1(0(0(x1)))))) 3(0(1(0(x1)))) -> 3(1(5(2(0(0(x1)))))) 3(0(1(0(x1)))) -> 3(1(5(5(0(0(x1)))))) 3(0(1(0(x1)))) -> 3(2(2(1(0(0(x1)))))) 3(0(1(0(x1)))) -> 3(5(1(0(0(2(x1)))))) 3(0(1(0(x1)))) -> 3(5(1(5(0(0(x1)))))) 3(0(1(0(x1)))) -> 5(1(1(3(0(0(x1)))))) 3(4(1(0(x1)))) -> 3(1(2(4(0(x1))))) 3(4(1(0(x1)))) -> 3(1(4(0(2(x1))))) 3(4(1(0(x1)))) -> 3(1(5(4(0(x1))))) 3(4(1(0(x1)))) -> 3(4(2(1(0(x1))))) 3(4(1(0(x1)))) -> 3(1(1(5(4(0(x1)))))) 3(4(1(0(x1)))) -> 3(1(2(1(4(0(x1)))))) 3(4(1(0(x1)))) -> 3(1(2(5(4(0(x1)))))) 3(4(1(0(x1)))) -> 3(1(4(2(0(2(x1)))))) 3(4(1(0(x1)))) -> 3(1(5(4(0(2(x1)))))) 3(4(1(0(x1)))) -> 3(1(5(5(4(0(x1)))))) 3(4(1(0(x1)))) -> 3(4(2(1(1(0(x1)))))) 3(4(1(0(x1)))) -> 3(4(5(1(2(0(x1)))))) 0(1(4(1(0(x1))))) -> 0(1(1(4(0(2(x1)))))) 0(2(0(1(0(x1))))) -> 0(2(0(0(3(1(x1)))))) 0(2(0(1(0(x1))))) -> 2(0(0(0(3(1(x1)))))) 0(3(0(1(0(x1))))) -> 0(0(3(1(3(0(x1)))))) 0(3(0(1(0(x1))))) -> 0(0(3(3(1(0(x1)))))) 0(3(0(1(0(x1))))) -> 0(0(3(5(1(0(x1)))))) 0(3(0(1(0(x1))))) -> 2(0(0(3(1(0(x1)))))) 0(3(4(1(0(x1))))) -> 0(2(0(4(3(1(x1)))))) 0(5(0(1(0(x1))))) -> 0(0(0(1(5(2(x1)))))) 0(5(0(1(0(x1))))) -> 0(0(1(5(1(0(x1)))))) 0(5(0(1(0(x1))))) -> 0(2(0(0(1(5(x1)))))) 3(0(1(0(0(x1))))) -> 3(1(3(0(0(0(x1)))))) 3(0(1(1(0(x1))))) -> 3(1(0(1(2(0(x1)))))) 3(0(2(1(0(x1))))) -> 2(0(3(1(1(0(x1)))))) 3(0(2(1(0(x1))))) -> 2(3(1(5(0(0(x1)))))) 3(0(2(1(0(x1))))) -> 3(1(2(0(1(0(x1)))))) 3(0(2(1(0(x1))))) -> 3(1(2(0(5(0(x1)))))) 3(0(5(1(0(x1))))) -> 3(1(5(2(0(0(x1)))))) 3(1(0(1(0(x1))))) -> 2(0(3(1(1(0(x1)))))) 3(1(0(1(0(x1))))) -> 3(1(1(1(0(0(x1)))))) 3(1(0(1(0(x1))))) -> 3(1(2(1(0(0(x1)))))) 3(1(4(1(0(x1))))) -> 3(1(2(1(4(0(x1)))))) 3(1(4(1(0(x1))))) -> 3(1(5(1(4(0(x1)))))) 3(2(0(1(0(x1))))) -> 0(2(3(1(5(0(x1)))))) 3(2(0(1(0(x1))))) -> 2(0(3(1(1(0(x1)))))) 3(3(0(1(0(x1))))) -> 3(1(2(0(3(0(x1)))))) 3(3(0(1(0(x1))))) -> 3(1(2(3(0(0(x1)))))) 3(3(4(1(0(x1))))) -> 3(1(2(4(3(0(x1)))))) 3(3(4(1(0(x1))))) -> 3(1(3(4(0(2(x1)))))) 3(3(4(1(0(x1))))) -> 3(1(4(3(1(0(x1)))))) 3(4(0(1(0(x1))))) -> 0(2(4(1(3(0(x1)))))) 3(4(0(1(0(x1))))) -> 3(1(4(0(0(2(x1)))))) 3(4(0(1(0(x1))))) -> 3(2(0(4(1(0(x1)))))) 3(4(4(1(0(x1))))) -> 3(1(1(4(4(0(x1)))))) Proof: Bounds Processor: bound: 0 enrichment: match automaton: final states: {202,201,198,195,192,189,185,182,178,174,171,169,167, 162,158,157,154,151,148,142,139,134,130,128,124,121, 116,114,112,108,104,101,98,94,91,87,85,82,79,76,72, 68,66,64,61,58,55,53,48,44,42,41,39,37,34,31,27,22, 19,14,8,1} transitions: 00(119) -> 120* 00(122) -> 123* 00(13) -> 8* 00(144) -> 145* 00(145) -> 146* 00(5) -> 6* 00(109) -> 152* 00(16) -> 17* 00(40) -> 129* 00(126) -> 127* 00(120) -> 116* 00(20) -> 40* 00(127) -> 124* 00(15) -> 16* 00(7) -> 1* 00(137) -> 138* 00(23) -> 24* 00(140) -> 141* 00(136) -> 137* 00(141) -> 139* 00(6) -> 115* 00(147) -> 142* 00(11) -> 12* 00(17) -> 18* 00(138) -> 134* 00(155) -> 156* 00(21) -> 19* 00(4) -> 5* 00(131) -> 132* 00(24) -> 25* 00(113) -> 112* 00(197) -> 195* 00(49) -> 50* 00(10) -> 159* 00(133) -> 130* 00(9) -> 28* 00(117) -> 179* 00(123) -> 121* 00(28) -> 45* 00(177) -> 174* 00(163) -> 164* 00(2) -> 9* f60() -> 2* 50(10) -> 125* 50(29) -> 38* 50(35) -> 59* 50(28) -> 35* 50(36) -> 67* 50(45) -> 46* 50(26) -> 65* 50(2) -> 143* 50(80) -> 102* 50(71) -> 68* 50(109) -> 110* 50(50) -> 51* 50(23) -> 135* 50(9) -> 163* 50(32) -> 56* 50(73) -> 80* 50(40) -> 39* 50(88) -> 172* 50(77) -> 99* 40(73) -> 203* 40(24) -> 77* 40(110) -> 111* 40(95) -> 96* 40(9) -> 73* 40(83) -> 84* 40(20) -> 193* 40(10) -> 11* 40(118) -> 196* 40(4) -> 131* 40(117) -> 186* 40(106) -> 107* 40(25) -> 199* 20(186) -> 187* 20(24) -> 95* 20(2) -> 23* 20(10) -> 83* 20(62) -> 63* 20(115) -> 114* 20(20) -> 21* 20(80) -> 92* 20(146) -> 147* 20(12) -> 13* 20(196) -> 197* 20(9) -> 49* 20(69) -> 183* 20(164) -> 165* 20(40) -> 43* 20(3) -> 15* 20(28) -> 32* 20(18) -> 14* 20(29) -> 62* 20(88) -> 89* 20(129) -> 128* 20(176) -> 177* 20(43) -> 42* 20(6) -> 7* 20(105) -> 106* 20(34) -> 157* 20(132) -> 133* 20(179) -> 180* 20(156) -> 154* 20(19) -> 41* 20(159) -> 160* 20(73) -> 74* 10(35) -> 36* 10(30) -> 168* 10(149) -> 150* 10(96) -> 97* 10(81) -> 86* 10(29) -> 30* 10(10) -> 105* 10(49) -> 109* 10(38) -> 54* 10(180) -> 181* 10(204) -> 205* 10(69) -> 70* 10(62) -> 170* 10(56) -> 57* 10(163) -> 175* 10(183) -> 184* 10(143) -> 144* 10(125) -> 140* 10(99) -> 100* 10(9) -> 10* 10(92) -> 93* 10(172) -> 173* 10(135) -> 136* 10(199) -> 200* 10(203) -> 204* 10(187) -> 188* 10(190) -> 191* 10(89) -> 90* 10(70) -> 71* 10(165) -> 166* 10(80) -> 81* 10(77) -> 78* 10(46) -> 47* 10(59) -> 60* 10(28) -> 29* 10(32) -> 33* 10(193) -> 194* 10(51) -> 52* 10(152) -> 153* 10(102) -> 103* 10(74) -> 75* 10(160) -> 161* 10(117) -> 118* 10(25) -> 26* 10(78) -> 113* 10(2) -> 3* 10(73) -> 88* 30(188) -> 185* 30(153) -> 151* 30(38) -> 37* 30(103) -> 101* 30(54) -> 53* 30(100) -> 98* 30(194) -> 192* 30(20) -> 122* 30(168) -> 167* 30(57) -> 55* 30(47) -> 44* 30(36) -> 34* 30(28) -> 69* 30(181) -> 178* 30(191) -> 189* 30(63) -> 61* 30(90) -> 87* 30(10) -> 20* 30(107) -> 104* 30(81) -> 79* 30(13) -> 201* 30(97) -> 94* 30(205) -> 202* 30(161) -> 158* 30(75) -> 72* 30(84) -> 82* 30(60) -> 58* 30(118) -> 119* 30(9) -> 117* 30(170) -> 169* 30(111) -> 108* 30(52) -> 48* 30(93) -> 91* 30(26) -> 22* 30(150) -> 148* 30(184) -> 182* 30(77) -> 190* 30(125) -> 126* 30(45) -> 149* 30(33) -> 31* 30(86) -> 85* 30(3) -> 4* 30(105) -> 155* 30(30) -> 27* 30(200) -> 198* 30(78) -> 76* 30(166) -> 162* 30(173) -> 171* 30(65) -> 64* 30(67) -> 66* 30(175) -> 176* 151 -> 117* 27 -> 117* 19 -> 117* 142 -> 9,164 148 -> 117* 68 -> 117* 154 -> 4,20,117 48 -> 117* 158 -> 117* 162 -> 117* 64 -> 117* 42 -> 117* 169 -> 4,20 112 -> 9* 14 -> 9,28 114 -> 9,24,50 66 -> 117* 53 -> 117* 124 -> 9,179 22 -> 117* 116 -> 9,179 171 -> 4* 121 -> 9,179 58 -> 117* 44 -> 117* 139 -> 9,164 8 -> 9,28 1 -> 24,50,9,28 31 -> 117* 130 -> 9* 55 -> 117* 34 -> 117* 37 -> 117* 134 -> 9,164 39 -> 117* 41 -> 117* 167 -> 4,20 87 -> 4* 128 -> 9,179 61 -> 117* 157 -> 117* problem: Qed