9.83/2.90 YES 9.83/2.91 9.83/2.91 Problem: 9.83/2.91 0(0(1(2(x1)))) -> 0(2(0(1(1(x1))))) 9.83/2.91 0(1(2(2(x1)))) -> 0(2(2(1(0(x1))))) 9.83/2.91 0(1(2(2(x1)))) -> 1(0(2(2(0(x1))))) 9.83/2.91 0(1(2(3(x1)))) -> 0(2(0(1(3(x1))))) 9.83/2.91 0(1(2(3(x1)))) -> 0(2(3(3(1(x1))))) 9.83/2.91 0(2(1(2(x1)))) -> 0(2(2(0(1(x1))))) 9.83/2.91 0(2(1(2(x1)))) -> 0(2(2(2(1(x1))))) 9.83/2.91 0(2(1(2(x1)))) -> 0(2(2(2(1(1(x1)))))) 9.83/2.91 0(3(2(2(x1)))) -> 3(4(0(2(2(x1))))) 9.83/2.91 0(3(2(2(x1)))) -> 0(2(2(2(2(3(x1)))))) 9.83/2.91 0(4(1(2(x1)))) -> 0(2(2(1(4(x1))))) 9.83/2.91 0(4(1(2(x1)))) -> 4(0(2(0(1(x1))))) 9.83/2.91 0(5(0(1(x1)))) -> 0(2(0(2(5(1(x1)))))) 9.83/2.91 0(5(0(5(x1)))) -> 0(2(0(5(5(x1))))) 9.83/2.91 0(5(2(1(x1)))) -> 0(2(2(5(1(x1))))) 9.83/2.91 0(5(2(5(x1)))) -> 0(2(2(5(5(x1))))) 9.83/2.91 0(5(4(2(x1)))) -> 4(0(2(2(0(5(x1)))))) 9.83/2.91 2(1(0(3(x1)))) -> 4(0(2(2(3(1(x1)))))) 9.83/2.91 2(1(0(4(x1)))) -> 1(4(0(2(2(2(x1)))))) 9.83/2.91 2(5(4(2(x1)))) -> 4(0(2(2(5(x1))))) 9.83/2.91 0(0(1(0(4(x1))))) -> 0(0(2(0(1(4(x1)))))) 9.83/2.91 0(0(5(4(2(x1))))) -> 0(4(0(0(2(5(x1)))))) 9.83/2.91 0(1(0(1(2(x1))))) -> 0(2(0(1(4(1(x1)))))) 9.83/2.91 0(1(2(0(3(x1))))) -> 0(2(0(4(1(3(x1)))))) 9.83/2.91 0(1(2(2(2(x1))))) -> 0(2(2(2(1(2(x1)))))) 9.83/2.91 0(1(2(3(2(x1))))) -> 1(3(4(0(2(2(x1)))))) 9.83/2.91 0(1(3(2(3(x1))))) -> 0(0(2(3(3(1(x1)))))) 9.83/2.91 0(1(3(4(2(x1))))) -> 0(2(3(4(1(1(x1)))))) 9.83/2.91 0(2(1(0(1(x1))))) -> 0(0(2(0(1(1(x1)))))) 9.83/2.91 0(2(1(2(2(x1))))) -> 0(2(0(2(2(1(x1)))))) 9.83/2.91 0(2(3(0(5(x1))))) -> 0(2(0(0(5(3(x1)))))) 9.83/2.91 0(3(0(1(3(x1))))) -> 0(0(4(3(1(3(x1)))))) 9.83/2.91 0(3(0(4(1(x1))))) -> 0(0(1(4(4(3(x1)))))) 9.83/2.91 0(3(2(0(4(x1))))) -> 4(0(0(2(3(4(x1)))))) 9.83/2.91 0(4(5(2(3(x1))))) -> 0(2(2(3(4(5(x1)))))) 9.83/2.91 0(5(0(0(3(x1))))) -> 0(2(0(3(0(5(x1)))))) 9.83/2.91 0(5(0(1(2(x1))))) -> 0(0(2(0(1(5(x1)))))) 9.83/2.91 0(5(1(4(2(x1))))) -> 0(2(0(1(4(5(x1)))))) 9.83/2.91 0(5(2(5(1(x1))))) -> 0(2(0(5(5(1(x1)))))) 9.83/2.91 2(1(0(0(4(x1))))) -> 1(4(4(0(0(2(x1)))))) 9.83/2.91 2(5(0(0(3(x1))))) -> 0(2(0(0(5(3(x1)))))) 9.83/2.91 2(5(3(0(1(x1))))) -> 5(0(2(2(3(1(x1)))))) 9.83/2.91 5(0(1(2(2(x1))))) -> 5(1(0(2(0(2(x1)))))) 9.83/2.91 5(2(0(1(2(x1))))) -> 1(5(4(0(2(2(x1)))))) 9.83/2.91 5(2(1(0(1(x1))))) -> 0(2(3(1(5(1(x1)))))) 9.83/2.91 5(2(3(0(1(x1))))) -> 1(5(0(2(2(3(x1)))))) 9.83/2.91 5(3(0(4(1(x1))))) -> 4(5(0(2(3(1(x1)))))) 9.83/2.91 9.83/2.91 Proof: 9.83/2.91 String Reversal Processor: 9.83/2.91 2(1(0(0(x1)))) -> 1(1(0(2(0(x1))))) 9.83/2.91 2(2(1(0(x1)))) -> 0(1(2(2(0(x1))))) 9.83/2.91 2(2(1(0(x1)))) -> 0(2(2(0(1(x1))))) 9.83/2.91 3(2(1(0(x1)))) -> 3(1(0(2(0(x1))))) 9.83/2.91 3(2(1(0(x1)))) -> 1(3(3(2(0(x1))))) 9.83/2.91 2(1(2(0(x1)))) -> 1(0(2(2(0(x1))))) 9.83/2.91 2(1(2(0(x1)))) -> 1(2(2(2(0(x1))))) 9.83/2.91 2(1(2(0(x1)))) -> 1(1(2(2(2(0(x1)))))) 9.83/2.91 2(2(3(0(x1)))) -> 2(2(0(4(3(x1))))) 9.83/2.91 2(2(3(0(x1)))) -> 3(2(2(2(2(0(x1)))))) 9.83/2.91 2(1(4(0(x1)))) -> 4(1(2(2(0(x1))))) 9.83/2.91 2(1(4(0(x1)))) -> 1(0(2(0(4(x1))))) 9.83/2.91 1(0(5(0(x1)))) -> 1(5(2(0(2(0(x1)))))) 9.83/2.91 5(0(5(0(x1)))) -> 5(5(0(2(0(x1))))) 9.83/2.91 1(2(5(0(x1)))) -> 1(5(2(2(0(x1))))) 9.83/2.91 5(2(5(0(x1)))) -> 5(5(2(2(0(x1))))) 9.83/2.91 2(4(5(0(x1)))) -> 5(0(2(2(0(4(x1)))))) 9.83/2.91 3(0(1(2(x1)))) -> 1(3(2(2(0(4(x1)))))) 9.83/2.91 4(0(1(2(x1)))) -> 2(2(2(0(4(1(x1)))))) 9.83/2.91 2(4(5(2(x1)))) -> 5(2(2(0(4(x1))))) 9.83/2.91 4(0(1(0(0(x1))))) -> 4(1(0(2(0(0(x1)))))) 9.83/2.91 2(4(5(0(0(x1))))) -> 5(2(0(0(4(0(x1)))))) 9.83/2.91 2(1(0(1(0(x1))))) -> 1(4(1(0(2(0(x1)))))) 9.83/2.91 3(0(2(1(0(x1))))) -> 3(1(4(0(2(0(x1)))))) 9.83/2.91 2(2(2(1(0(x1))))) -> 2(1(2(2(2(0(x1)))))) 9.83/2.91 2(3(2(1(0(x1))))) -> 2(2(0(4(3(1(x1)))))) 9.83/2.91 3(2(3(1(0(x1))))) -> 1(3(3(2(0(0(x1)))))) 9.83/2.91 2(4(3(1(0(x1))))) -> 1(1(4(3(2(0(x1)))))) 9.83/2.91 1(0(1(2(0(x1))))) -> 1(1(0(2(0(0(x1)))))) 9.83/2.91 2(2(1(2(0(x1))))) -> 1(2(2(0(2(0(x1)))))) 9.83/2.91 5(0(3(2(0(x1))))) -> 3(5(0(0(2(0(x1)))))) 9.83/2.91 3(1(0(3(0(x1))))) -> 3(1(3(4(0(0(x1)))))) 9.83/2.91 1(4(0(3(0(x1))))) -> 3(4(4(1(0(0(x1)))))) 9.83/2.91 4(0(2(3(0(x1))))) -> 4(3(2(0(0(4(x1)))))) 9.83/2.91 3(2(5(4(0(x1))))) -> 5(4(3(2(2(0(x1)))))) 9.83/2.91 3(0(0(5(0(x1))))) -> 5(0(3(0(2(0(x1)))))) 9.83/2.91 2(1(0(5(0(x1))))) -> 5(1(0(2(0(0(x1)))))) 9.83/2.91 2(4(1(5(0(x1))))) -> 5(4(1(0(2(0(x1)))))) 9.83/2.91 1(5(2(5(0(x1))))) -> 1(5(5(0(2(0(x1)))))) 9.83/2.91 4(0(0(1(2(x1))))) -> 2(0(0(4(4(1(x1)))))) 9.83/2.91 3(0(0(5(2(x1))))) -> 3(5(0(0(2(0(x1)))))) 9.83/2.91 1(0(3(5(2(x1))))) -> 1(3(2(2(0(5(x1)))))) 9.83/2.91 2(2(1(0(5(x1))))) -> 2(0(2(0(1(5(x1)))))) 9.83/2.91 2(1(0(2(5(x1))))) -> 2(2(0(4(5(1(x1)))))) 9.83/2.91 1(0(1(2(5(x1))))) -> 1(5(1(3(2(0(x1)))))) 9.83/2.91 1(0(3(2(5(x1))))) -> 3(2(2(0(5(1(x1)))))) 9.83/2.91 1(4(0(3(5(x1))))) -> 1(3(2(0(5(4(x1)))))) 9.83/2.91 Bounds Processor: 9.83/2.91 bound: 0 9.83/2.91 enrichment: match 9.83/2.91 automaton: 9.83/2.91 final states: {137,133,130,125,120,114,110,109,108,107,104,101,97, 9.83/2.91 93,89,86,84,83,80,77,72,71,68,66,61,56,55,50,48,45, 9.83/2.92 44,42,40,37,32,31,29,24,23,21,19,16,15,10,7,1} 9.83/2.92 transitions: 9.83/2.92 f60() -> 2* 9.83/2.92 10(60) -> 83* 9.83/2.92 10(40) -> 109* 9.83/2.92 10(20) -> 19* 9.83/2.92 10(5) -> 6* 9.83/2.92 10(132) -> 130* 9.83/2.92 10(82) -> 80* 9.83/2.92 10(67) -> 66* 9.83/2.92 10(57) -> 94* 9.83/2.92 10(22) -> 21* 9.83/2.92 10(17) -> 131* 9.83/2.92 10(2) -> 11* 9.83/2.92 10(119) -> 114* 9.83/2.92 10(79) -> 77* 9.83/2.92 10(69) -> 70* 9.83/2.92 10(59) -> 60* 9.83/2.92 10(49) -> 48* 9.83/2.92 10(39) -> 37* 9.83/2.92 10(141) -> 137* 9.83/2.92 10(91) -> 92* 9.83/2.92 10(81) -> 82* 9.83/2.92 10(36) -> 32* 9.83/2.92 10(21) -> 23* 9.83/2.92 10(6) -> 1* 9.83/2.92 10(43) -> 42* 9.83/2.92 10(18) -> 16* 9.83/2.92 10(8) -> 9* 9.83/2.92 10(115) -> 121* 9.83/2.92 10(85) -> 84* 9.83/2.92 00(35) -> 36* 9.83/2.92 00(5) -> 87* 9.83/2.92 00(127) -> 128* 9.83/2.92 00(112) -> 113* 9.83/2.92 00(62) -> 63* 9.83/2.92 00(2) -> 3* 9.83/2.92 00(74) -> 75* 9.83/2.92 00(34) -> 98* 9.83/2.92 00(14) -> 10* 9.83/2.92 00(9) -> 7* 9.83/2.92 00(4) -> 5* 9.83/2.92 00(126) -> 134* 9.83/2.92 00(121) -> 122* 9.83/2.92 00(111) -> 112* 9.83/2.92 00(51) -> 52* 9.83/2.92 00(46) -> 47* 9.83/2.92 00(26) -> 27* 9.83/2.92 00(11) -> 12* 9.83/2.92 00(138) -> 139* 9.83/2.92 00(123) -> 124* 9.83/2.92 00(63) -> 64* 9.83/2.92 00(58) -> 59* 9.83/2.92 00(33) -> 34* 9.83/2.92 00(8) -> 20* 9.83/2.92 00(3) -> 57* 9.83/2.92 00(115) -> 116* 9.83/2.92 00(105) -> 106* 9.83/2.92 20(75) -> 76* 9.83/2.92 20(35) -> 46* 9.83/2.92 20(5) -> 38* 9.83/2.92 20(122) -> 123* 9.83/2.92 20(117) -> 118* 9.83/2.92 20(57) -> 58* 9.83/2.92 20(52) -> 53* 9.83/2.92 20(27) -> 28* 9.83/2.92 20(22) -> 30* 9.83/2.92 20(12) -> 13* 9.83/2.92 20(139) -> 140* 9.83/2.92 20(134) -> 135* 9.83/2.92 20(129) -> 125* 9.83/2.92 20(124) -> 120* 9.83/2.92 20(64) -> 65* 9.83/2.92 20(54) -> 50* 9.83/2.92 20(34) -> 35* 9.83/2.92 20(4) -> 8* 9.83/2.92 20(116) -> 117* 9.83/2.92 20(76) -> 72* 9.83/2.92 20(21) -> 71* 9.83/2.92 20(128) -> 129* 9.83/2.92 20(113) -> 110* 9.83/2.92 20(98) -> 99* 9.83/2.92 20(53) -> 54* 9.83/2.92 20(38) -> 85* 9.83/2.92 20(28) -> 24* 9.83/2.92 20(13) -> 14* 9.83/2.92 20(8) -> 22* 9.83/2.92 20(3) -> 4* 9.83/2.92 20(135) -> 136* 9.83/2.92 30(70) -> 68* 9.83/2.92 30(30) -> 29* 9.83/2.92 30(5) -> 105* 9.83/2.92 30(92) -> 89* 9.83/2.92 30(17) -> 18* 9.83/2.92 30(2) -> 25* 9.83/2.92 30(99) -> 100* 9.83/2.92 30(4) -> 17* 9.83/2.92 30(136) -> 133* 9.83/2.92 30(96) -> 93* 9.83/2.92 30(46) -> 49* 9.83/2.92 30(11) -> 73* 9.83/2.92 30(6) -> 15* 9.83/2.92 30(118) -> 119* 9.83/2.92 30(88) -> 86* 9.83/2.92 30(78) -> 79* 9.83/2.92 30(58) -> 78* 9.83/2.92 30(8) -> 102* 9.83/2.92 30(140) -> 141* 9.83/2.92 30(90) -> 91* 9.83/2.92 40(60) -> 56* 9.83/2.92 40(25) -> 26* 9.83/2.92 40(5) -> 69* 9.83/2.92 40(102) -> 103* 9.83/2.92 40(57) -> 90* 9.83/2.92 40(17) -> 81* 9.83/2.92 40(2) -> 33* 9.83/2.92 40(94) -> 95* 9.83/2.92 40(9) -> 31* 9.83/2.92 40(126) -> 127* 9.83/2.92 40(51) -> 111* 9.83/2.92 40(11) -> 51* 9.83/2.92 40(6) -> 67* 9.83/2.92 40(73) -> 74* 9.83/2.92 40(3) -> 62* 9.83/2.92 40(100) -> 97* 9.83/2.92 40(95) -> 96* 9.83/2.92 50(65) -> 61* 9.83/2.92 50(60) -> 107* 9.83/2.92 50(5) -> 41* 9.83/2.92 50(87) -> 88* 9.83/2.92 50(67) -> 108* 9.83/2.92 50(47) -> 45* 9.83/2.92 50(2) -> 115* 9.83/2.92 50(131) -> 132* 9.83/2.92 50(106) -> 104* 9.83/2.92 50(46) -> 55* 9.83/2.92 50(41) -> 40* 9.83/2.92 50(11) -> 126* 9.83/2.92 50(103) -> 101* 9.83/2.92 50(43) -> 44* 9.83/2.92 50(38) -> 39* 9.83/2.92 50(33) -> 138* 9.83/2.92 50(8) -> 43* 9.83/2.92 15 -> 25* 9.83/2.92 16 -> 25* 9.83/2.92 37 -> 11* 9.83/2.92 40 -> 115* 9.83/2.92 42 -> 11* 9.83/2.92 44 -> 115* 9.83/2.92 48 -> 25* 9.83/2.92 50 -> 33,62 9.83/2.92 56 -> 33,62 9.83/2.92 68 -> 25* 9.83/2.92 77 -> 25* 9.83/2.92 83 -> 11* 9.83/2.92 86 -> 25,115 9.83/2.92 89 -> 25,73 9.83/2.92 93 -> 11* 9.83/2.92 97 -> 33,62 9.83/2.92 101 -> 25* 9.83/2.92 104 -> 25* 9.83/2.92 109 -> 11* 9.83/2.92 110 -> 33,62,90 9.83/2.92 114 -> 11* 9.83/2.92 130 -> 11* 9.83/2.92 133 -> 11* 9.83/2.92 137 -> 11* 9.83/2.92 problem: 9.83/2.92 9.83/2.92 Qed 9.83/2.92 EOF