31.92/8.53 YES 31.92/8.55 31.92/8.55 Problem: 31.92/8.55 0(0(1(x1))) -> 0(0(2(1(3(x1))))) 31.92/8.55 0(0(1(x1))) -> 0(0(2(2(3(1(x1)))))) 31.92/8.55 0(4(1(x1))) -> 0(4(2(2(1(x1))))) 31.92/8.55 0(4(1(x1))) -> 0(2(3(1(4(2(x1)))))) 31.92/8.55 1(0(1(x1))) -> 0(2(1(1(x1)))) 31.92/8.55 1(0(1(x1))) -> 0(2(1(1(2(x1))))) 31.92/8.55 1(0(1(x1))) -> 1(0(3(2(1(x1))))) 31.92/8.55 1(4(0(x1))) -> 1(0(3(2(4(2(x1)))))) 31.92/8.55 1(4(1(x1))) -> 4(2(1(1(x1)))) 31.92/8.55 1(4(1(x1))) -> 4(2(1(1(2(1(x1)))))) 31.92/8.55 4(0(1(x1))) -> 4(0(2(1(x1)))) 31.92/8.55 5(0(1(x1))) -> 5(0(2(1(x1)))) 31.92/8.55 5(0(1(x1))) -> 0(2(1(5(3(x1))))) 31.92/8.55 5(0(1(x1))) -> 0(3(2(1(5(5(x1)))))) 31.92/8.55 5(0(1(x1))) -> 3(0(2(3(5(1(x1)))))) 31.92/8.55 5(0(5(x1))) -> 0(3(2(5(3(5(x1)))))) 31.92/8.55 5(4(1(x1))) -> 2(4(2(5(1(3(x1)))))) 31.92/8.55 5(4(1(x1))) -> 4(5(2(1(3(3(x1)))))) 31.92/8.55 0(0(4(5(x1)))) -> 0(5(0(2(4(2(x1)))))) 31.92/8.55 0(1(2(0(x1)))) -> 2(0(2(1(0(x1))))) 31.92/8.55 0(2(0(1(x1)))) -> 0(0(2(1(3(x1))))) 31.92/8.55 0(3(4(0(x1)))) -> 3(2(4(0(0(3(x1)))))) 31.92/8.55 0(4(0(4(x1)))) -> 0(0(3(2(4(4(x1)))))) 31.92/8.55 1(0(1(4(x1)))) -> 2(3(1(1(4(0(x1)))))) 31.92/8.55 1(0(3(1(x1)))) -> 4(2(3(1(1(0(x1)))))) 31.92/8.55 1(2(0(4(x1)))) -> 1(4(2(0(3(2(x1)))))) 31.92/8.55 1(3(0(4(x1)))) -> 4(0(3(2(1(3(x1)))))) 31.92/8.55 1(4(1(5(x1)))) -> 2(1(2(5(1(4(x1)))))) 31.92/8.55 4(0(5(1(x1)))) -> 0(2(4(2(1(5(x1)))))) 31.92/8.55 4(1(0(0(x1)))) -> 3(2(1(4(0(0(x1)))))) 31.92/8.55 4(1(0(4(x1)))) -> 4(4(0(2(1(x1))))) 31.92/8.55 5(0(0(1(x1)))) -> 0(3(2(5(1(0(x1)))))) 31.92/8.55 5(0(3(1(x1)))) -> 0(5(3(2(1(x1))))) 31.92/8.55 5(0(3(1(x1)))) -> 0(3(5(2(2(1(x1)))))) 31.92/8.55 5(0(5(1(x1)))) -> 5(2(5(3(1(0(x1)))))) 31.92/8.55 5(2(4(1(x1)))) -> 2(1(4(2(5(x1))))) 31.92/8.55 5(4(1(5(x1)))) -> 4(5(5(2(1(x1))))) 31.92/8.55 5(4(1(5(x1)))) -> 2(1(5(4(2(5(x1)))))) 31.92/8.55 5(4(3(1(x1)))) -> 5(4(2(1(3(x1))))) 31.92/8.55 5(4(3(1(x1)))) -> 3(5(2(4(2(1(x1)))))) 31.92/8.55 5(4(3(1(x1)))) -> 5(2(4(3(2(1(x1)))))) 31.92/8.55 5(5(0(4(x1)))) -> 5(0(2(5(4(2(x1)))))) 31.92/8.55 0(0(3(3(1(x1))))) -> 0(3(0(1(2(3(x1)))))) 31.92/8.55 0(2(4(3(1(x1))))) -> 0(2(3(1(4(2(x1)))))) 31.92/8.55 0(5(4(1(1(x1))))) -> 4(0(2(5(1(1(x1)))))) 31.92/8.55 1(2(4(3(1(x1))))) -> 1(2(3(3(1(4(x1)))))) 31.92/8.55 4(0(0(3(1(x1))))) -> 4(0(3(2(1(0(x1)))))) 31.92/8.55 4(0(0(3(1(x1))))) -> 4(3(2(0(0(1(x1)))))) 31.92/8.55 5(1(0(0(5(x1))))) -> 5(0(0(2(1(5(x1)))))) 31.92/8.55 5(4(2(0(1(x1))))) -> 2(5(4(0(2(1(x1)))))) 31.92/8.55 31.92/8.55 Proof: 31.92/8.55 String Reversal Processor: 31.92/8.55 1(0(0(x1))) -> 3(1(2(0(0(x1))))) 31.92/8.55 1(0(0(x1))) -> 1(3(2(2(0(0(x1)))))) 31.92/8.55 1(4(0(x1))) -> 1(2(2(4(0(x1))))) 31.92/8.55 1(4(0(x1))) -> 2(4(1(3(2(0(x1)))))) 31.92/8.55 1(0(1(x1))) -> 1(1(2(0(x1)))) 31.92/8.55 1(0(1(x1))) -> 2(1(1(2(0(x1))))) 31.92/8.55 1(0(1(x1))) -> 1(2(3(0(1(x1))))) 31.92/8.55 0(4(1(x1))) -> 2(4(2(3(0(1(x1)))))) 31.92/8.55 1(4(1(x1))) -> 1(1(2(4(x1)))) 31.92/8.55 1(4(1(x1))) -> 1(2(1(1(2(4(x1)))))) 31.92/8.55 1(0(4(x1))) -> 1(2(0(4(x1)))) 31.92/8.55 1(0(5(x1))) -> 1(2(0(5(x1)))) 31.92/8.55 1(0(5(x1))) -> 3(5(1(2(0(x1))))) 31.92/8.55 1(0(5(x1))) -> 5(5(1(2(3(0(x1)))))) 31.92/8.55 1(0(5(x1))) -> 1(5(3(2(0(3(x1)))))) 31.92/8.55 5(0(5(x1))) -> 5(3(5(2(3(0(x1)))))) 31.92/8.55 1(4(5(x1))) -> 3(1(5(2(4(2(x1)))))) 31.92/8.55 1(4(5(x1))) -> 3(3(1(2(5(4(x1)))))) 31.92/8.55 5(4(0(0(x1)))) -> 2(4(2(0(5(0(x1)))))) 31.92/8.55 0(2(1(0(x1)))) -> 0(1(2(0(2(x1))))) 31.92/8.55 1(0(2(0(x1)))) -> 3(1(2(0(0(x1))))) 31.92/8.55 0(4(3(0(x1)))) -> 3(0(0(4(2(3(x1)))))) 31.92/8.55 4(0(4(0(x1)))) -> 4(4(2(3(0(0(x1)))))) 31.92/8.55 4(1(0(1(x1)))) -> 0(4(1(1(3(2(x1)))))) 31.92/8.55 1(3(0(1(x1)))) -> 0(1(1(3(2(4(x1)))))) 31.92/8.55 4(0(2(1(x1)))) -> 2(3(0(2(4(1(x1)))))) 31.92/8.55 4(0(3(1(x1)))) -> 3(1(2(3(0(4(x1)))))) 31.92/8.55 5(1(4(1(x1)))) -> 4(1(5(2(1(2(x1)))))) 31.92/8.55 1(5(0(4(x1)))) -> 5(1(2(4(2(0(x1)))))) 31.92/8.55 0(0(1(4(x1)))) -> 0(0(4(1(2(3(x1)))))) 31.92/8.55 4(0(1(4(x1)))) -> 1(2(0(4(4(x1))))) 31.92/8.55 1(0(0(5(x1)))) -> 0(1(5(2(3(0(x1)))))) 31.92/8.55 1(3(0(5(x1)))) -> 1(2(3(5(0(x1))))) 31.92/8.55 1(3(0(5(x1)))) -> 1(2(2(5(3(0(x1)))))) 31.92/8.55 1(5(0(5(x1)))) -> 0(1(3(5(2(5(x1)))))) 31.92/8.55 1(4(2(5(x1)))) -> 5(2(4(1(2(x1))))) 31.92/8.55 5(1(4(5(x1)))) -> 1(2(5(5(4(x1))))) 31.92/8.55 5(1(4(5(x1)))) -> 5(2(4(5(1(2(x1)))))) 31.92/8.55 1(3(4(5(x1)))) -> 3(1(2(4(5(x1))))) 31.92/8.55 1(3(4(5(x1)))) -> 1(2(4(2(5(3(x1)))))) 31.92/8.55 1(3(4(5(x1)))) -> 1(2(3(4(2(5(x1)))))) 31.92/8.55 4(0(5(5(x1)))) -> 2(4(5(2(0(5(x1)))))) 31.92/8.55 1(3(3(0(0(x1))))) -> 3(2(1(0(3(0(x1)))))) 31.92/8.55 1(3(4(2(0(x1))))) -> 2(4(1(3(2(0(x1)))))) 31.92/8.55 1(1(4(5(0(x1))))) -> 1(1(5(2(0(4(x1)))))) 31.92/8.55 1(3(4(2(1(x1))))) -> 4(1(3(3(2(1(x1)))))) 31.92/8.55 1(3(0(0(4(x1))))) -> 0(1(2(3(0(4(x1)))))) 31.92/8.55 1(3(0(0(4(x1))))) -> 1(0(0(2(3(4(x1)))))) 31.92/8.55 5(0(0(1(5(x1))))) -> 5(1(2(0(0(5(x1)))))) 31.92/8.55 1(0(2(4(5(x1))))) -> 1(2(0(4(5(2(x1)))))) 31.92/8.55 Bounds Processor: 31.92/8.55 bound: 1 31.92/8.55 enrichment: match 31.92/8.55 automaton: 31.92/8.55 final states: {184,180,175,174,169,166,162,159,155,150,146,142,139, 31.92/8.55 136,131,127,124,122,118,114,110,105,101,96,92,87,83, 31.92/8.55 78,74,69,64,58,55,49,44,42,38,35,33,29,27,22,21,19, 31.92/8.55 14,10,7,1} 31.92/8.55 transitions: 31.92/8.55 f60() -> 2* 31.92/8.55 30(70) -> 125* 31.92/8.55 30(30) -> 176* 31.92/8.55 30(15) -> 16* 31.92/8.55 30(82) -> 78* 31.92/8.55 30(67) -> 68* 31.92/8.55 30(52) -> 53* 31.92/8.55 30(2) -> 50* 31.92/8.55 30(149) -> 146* 31.92/8.55 30(104) -> 101* 31.92/8.55 30(99) -> 100* 31.92/8.55 30(59) -> 88* 31.92/8.55 30(24) -> 25* 31.92/8.55 30(4) -> 84* 31.92/8.55 30(171) -> 172* 31.92/8.55 30(156) -> 157* 31.92/8.55 30(56) -> 57* 31.92/8.55 30(36) -> 102* 31.92/8.55 30(31) -> 93* 31.92/8.55 30(6) -> 1* 31.92/8.55 30(133) -> 134* 31.92/8.55 30(68) -> 64* 31.92/8.55 30(63) -> 58* 31.92/8.55 30(43) -> 42* 31.92/8.55 30(8) -> 9* 31.92/8.55 30(3) -> 45* 31.92/8.55 30(170) -> 171* 31.92/8.55 30(165) -> 162* 31.92/8.55 10(20) -> 19* 31.92/8.55 10(15) -> 20* 31.92/8.55 10(5) -> 6* 31.92/8.55 10(182) -> 183* 31.92/8.55 10(172) -> 173* 31.92/8.55 10(167) -> 168* 31.92/8.55 10(112) -> 113* 31.92/8.55 10(62) -> 63* 31.92/8.55 10(37) -> 35* 31.92/8.55 10(32) -> 29* 31.92/8.55 10(2) -> 23* 31.92/8.55 10(179) -> 175* 31.92/8.55 10(154) -> 150* 31.92/8.55 10(134) -> 135* 31.92/8.55 10(94) -> 95* 31.92/8.55 10(89) -> 90* 31.92/8.55 10(79) -> 115* 31.92/8.55 10(59) -> 106* 31.92/8.55 10(54) -> 49* 31.92/8.55 10(34) -> 33* 31.92/8.55 10(9) -> 7* 31.92/8.55 10(141) -> 139* 31.92/8.55 10(126) -> 124* 31.92/8.55 10(121) -> 118* 31.92/8.55 10(76) -> 77* 31.92/8.55 10(66) -> 67* 31.92/8.55 10(56) -> 123* 31.92/8.55 10(46) -> 47* 31.92/8.55 10(41) -> 38* 31.92/8.55 10(31) -> 32* 31.92/8.55 10(26) -> 22* 31.92/8.55 10(16) -> 17* 31.92/8.55 10(188) -> 184* 31.92/8.55 10(168) -> 166* 31.92/8.55 10(163) -> 164* 31.92/8.55 10(158) -> 155* 31.92/8.55 10(148) -> 149* 31.92/8.55 10(108) -> 109* 31.92/8.55 10(103) -> 104* 31.92/8.55 10(93) -> 94* 31.92/8.55 10(88) -> 89* 31.92/8.55 10(13) -> 10* 31.92/8.55 10(130) -> 127* 31.92/8.55 20(75) -> 76* 31.92/8.55 20(65) -> 66* 31.92/8.55 20(60) -> 61* 31.92/8.55 20(50) -> 79* 31.92/8.55 20(45) -> 46* 31.92/8.55 20(40) -> 41* 31.92/8.55 20(30) -> 31* 31.92/8.55 20(25) -> 26* 31.92/8.55 20(5) -> 8* 31.92/8.55 20(187) -> 188* 31.92/8.55 20(157) -> 158* 31.92/8.55 20(147) -> 148* 31.92/8.55 20(137) -> 138* 31.92/8.55 20(102) -> 103* 31.92/8.55 20(97) -> 98* 31.92/8.55 20(12) -> 13* 31.92/8.55 20(2) -> 59* 31.92/8.55 20(164) -> 165* 31.92/8.55 20(144) -> 145* 31.92/8.55 20(129) -> 130* 31.92/8.55 20(84) -> 85* 31.92/8.55 20(39) -> 132* 31.92/8.55 20(29) -> 34* 31.92/8.55 20(19) -> 21* 31.92/8.55 20(4) -> 5* 31.92/8.55 20(181) -> 182* 31.92/8.55 20(176) -> 177* 31.92/8.55 20(161) -> 159* 31.92/8.55 20(151) -> 152* 31.92/8.55 20(111) -> 112* 31.92/8.55 20(106) -> 107* 31.92/8.55 20(71) -> 72* 31.92/8.55 20(51) -> 52* 31.92/8.55 20(36) -> 37* 31.92/8.55 20(11) -> 12* 31.92/8.55 20(153) -> 154* 31.92/8.55 20(128) -> 129* 31.92/8.55 20(73) -> 69* 31.92/8.55 20(28) -> 27* 31.92/8.55 20(23) -> 170* 31.92/8.55 20(18) -> 14* 31.92/8.55 20(3) -> 15* 31.92/8.55 20(140) -> 141* 31.92/8.55 20(125) -> 126* 31.92/8.55 20(120) -> 121* 31.92/8.55 20(100) -> 96* 31.92/8.55 00(80) -> 81* 31.92/8.55 00(70) -> 71* 31.92/8.55 00(50) -> 51* 31.92/8.55 00(45) -> 163* 31.92/8.55 00(40) -> 181* 31.92/8.55 00(30) -> 36* 31.92/8.55 00(177) -> 178* 31.92/8.55 00(117) -> 114* 31.92/8.55 00(77) -> 74* 31.92/8.55 00(2) -> 3* 31.92/8.55 00(119) -> 120* 31.92/8.55 00(104) -> 174* 31.92/8.55 00(59) -> 75* 31.92/8.55 00(39) -> 40* 31.92/8.55 00(186) -> 187* 31.92/8.55 00(116) -> 117* 31.92/8.55 00(91) -> 87* 31.92/8.55 00(81) -> 82* 31.92/8.55 00(178) -> 179* 31.92/8.55 00(123) -> 122* 31.92/8.55 00(98) -> 99* 31.92/8.55 00(23) -> 24* 31.92/8.55 00(3) -> 4* 31.92/8.55 00(135) -> 131* 31.92/8.55 00(95) -> 92* 31.92/8.55 40(30) -> 119* 31.92/8.55 40(15) -> 111* 31.92/8.55 40(152) -> 153* 31.92/8.55 40(132) -> 156* 31.92/8.55 40(72) -> 73* 31.92/8.55 40(17) -> 18* 31.92/8.55 40(2) -> 30* 31.92/8.55 40(109) -> 105* 31.92/8.55 40(79) -> 80* 31.92/8.55 40(59) -> 60* 31.92/8.55 40(39) -> 147* 31.92/8.55 40(106) -> 137* 31.92/8.55 40(86) -> 83* 31.92/8.55 40(26) -> 28* 31.92/8.55 40(173) -> 169* 31.92/8.55 40(143) -> 144* 31.92/8.55 40(23) -> 97* 31.92/8.55 40(3) -> 11* 31.92/8.55 40(185) -> 186* 31.92/8.55 40(160) -> 161* 31.92/8.55 40(115) -> 116* 31.92/8.55 40(90) -> 91* 31.92/8.55 40(85) -> 86* 31.92/8.55 50(65) -> 140* 31.92/8.55 50(50) -> 151* 31.92/8.55 50(45) -> 128* 31.92/8.55 50(30) -> 65* 31.92/8.55 50(20) -> 43* 31.92/8.55 50(132) -> 133* 31.92/8.55 50(107) -> 108* 31.92/8.55 50(57) -> 55* 31.92/8.55 50(47) -> 48* 31.92/8.55 50(37) -> 167* 31.92/8.55 50(2) -> 39* 31.92/8.55 50(59) -> 185* 31.92/8.55 50(106) -> 143* 31.92/8.55 50(61) -> 62* 31.92/8.55 50(46) -> 56* 31.92/8.55 50(41) -> 160* 31.92/8.55 50(183) -> 180* 31.92/8.55 50(138) -> 136* 31.92/8.55 50(113) -> 110* 31.92/8.55 50(53) -> 54* 31.92/8.55 50(48) -> 44* 31.92/8.55 50(3) -> 70* 31.92/8.55 50(145) -> 142* 31.92/8.55 21(277) -> 278* 31.92/8.55 21(247) -> 248* 31.92/8.55 21(197) -> 198* 31.92/8.55 21(249) -> 250* 31.92/8.55 21(219) -> 220* 31.92/8.55 21(261) -> 262* 31.92/8.55 21(226) -> 227* 31.92/8.55 21(221) -> 222* 31.92/8.55 21(201) -> 202* 31.92/8.55 21(263) -> 264* 31.92/8.55 21(228) -> 229* 31.92/8.55 21(275) -> 276* 31.92/8.55 41(262) -> 263* 31.92/8.55 41(227) -> 228* 31.92/8.55 41(276) -> 277* 31.92/8.55 41(248) -> 249* 31.92/8.55 41(220) -> 221* 31.92/8.55 31(202) -> 203* 31.92/8.55 31(274) -> 275* 31.92/8.55 31(199) -> 200* 31.92/8.55 31(246) -> 247* 31.92/8.55 31(218) -> 219* 31.92/8.55 31(260) -> 261* 31.92/8.55 31(225) -> 226* 31.92/8.55 01(217) -> 218* 31.92/8.55 01(259) -> 260* 31.92/8.55 01(224) -> 225* 31.92/8.55 01(196) -> 197* 31.92/8.55 01(273) -> 274* 31.92/8.55 01(245) -> 246* 31.92/8.55 01(195) -> 196* 31.92/8.55 11(272) -> 273* 31.92/8.55 11(244) -> 245* 31.92/8.55 11(216) -> 217* 31.92/8.55 11(258) -> 259* 31.92/8.55 11(223) -> 224* 31.92/8.55 11(203) -> 204* 31.92/8.55 11(198) -> 199* 31.92/8.55 1 -> 23* 31.92/8.55 7 -> 23* 31.92/8.55 10 -> 23* 31.92/8.55 14 -> 23* 31.92/8.55 19 -> 23* 31.92/8.55 21 -> 23* 31.92/8.55 22 -> 23* 31.92/8.55 27 -> 3,36 31.92/8.55 29 -> 23* 31.92/8.55 33 -> 23* 31.92/8.55 35 -> 23* 31.92/8.55 38 -> 23* 31.92/8.55 42 -> 23* 31.92/8.55 44 -> 23* 31.92/8.55 49 -> 23* 31.92/8.55 55 -> 39,70 31.92/8.55 58 -> 23* 31.92/8.55 64 -> 23* 31.92/8.55 69 -> 39,65 31.92/8.55 74 -> 3,75 31.92/8.55 78 -> 3,36 31.92/8.55 79 -> 223* 31.92/8.55 83 -> 30,11 31.92/8.55 87 -> 30,97 31.92/8.55 89 -> 216* 31.92/8.55 92 -> 23* 31.92/8.55 96 -> 30,11 31.92/8.55 101 -> 30,11 31.92/8.55 105 -> 39* 31.92/8.55 108 -> 244* 31.92/8.55 110 -> 23* 31.92/8.55 114 -> 3,4 31.92/8.55 118 -> 30,11 31.92/8.55 121 -> 258* 31.92/8.55 122 -> 23* 31.92/8.55 124 -> 23* 31.92/8.55 127 -> 23* 31.92/8.55 131 -> 23* 31.92/8.55 136 -> 23* 31.92/8.55 139 -> 39* 31.92/8.55 142 -> 39* 31.92/8.55 146 -> 23* 31.92/8.55 150 -> 23* 31.92/8.55 155 -> 23* 31.92/8.55 159 -> 30,11 31.92/8.55 162 -> 23* 31.92/8.55 166 -> 23* 31.92/8.55 169 -> 23* 31.92/8.55 172 -> 272* 31.92/8.55 174 -> 23* 31.92/8.55 175 -> 23* 31.92/8.55 177 -> 195* 31.92/8.55 180 -> 39,70 31.92/8.55 184 -> 23* 31.92/8.55 198 -> 201* 31.92/8.55 200 -> 175* 31.92/8.55 204 -> 175* 31.92/8.55 222 -> 87* 31.92/8.55 229 -> 117* 31.92/8.55 250 -> 40* 31.92/8.55 264 -> 120* 31.92/8.55 278 -> 24* 31.92/8.55 problem: 31.92/8.55 31.92/8.55 Qed 31.95/8.56 EOF