41.06/10.91 YES 41.40/10.92 41.40/10.92 Problem: 41.40/10.92 a(a(x1)) -> b(a(b(x1))) 41.40/10.92 a(a(a(x1))) -> a(b(a(b(a(x1))))) 41.40/10.92 a(b(a(x1))) -> b(b(a(b(b(x1))))) 41.40/10.92 a(a(a(a(x1)))) -> a(a(b(a(b(a(a(x1))))))) 41.40/10.92 a(a(b(a(x1)))) -> a(b(b(a(b(a(b(x1))))))) 41.40/10.92 a(b(a(a(x1)))) -> b(a(b(a(b(b(a(x1))))))) 41.40/10.92 a(b(b(a(x1)))) -> b(b(b(a(b(b(b(x1))))))) 41.40/10.92 a(a(a(a(a(x1))))) -> a(a(a(b(a(b(a(a(a(x1))))))))) 41.40/10.92 a(a(a(b(a(x1))))) -> a(a(b(b(a(b(a(a(b(x1))))))))) 41.40/10.92 a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(b(a(x1))))))))) 41.40/10.92 a(a(b(b(a(x1))))) -> a(b(b(b(a(b(a(b(b(x1))))))))) 41.40/10.92 a(b(a(a(a(x1))))) -> b(a(a(b(a(b(b(a(a(x1))))))))) 41.40/10.92 a(b(a(b(a(x1))))) -> b(a(b(b(a(b(b(a(b(x1))))))))) 41.40/10.92 a(b(b(a(a(x1))))) -> b(b(a(b(a(b(b(b(a(x1))))))))) 41.40/10.92 a(b(b(b(a(x1))))) -> b(b(b(b(a(b(b(b(b(x1))))))))) 41.40/10.92 41.40/10.92 Proof: 41.40/10.92 Matrix Interpretation Processor: dim=3 41.40/10.92 41.40/10.92 interpretation: 41.40/10.92 [1 0 0] 41.40/10.92 [b](x0) = [0 0 0]x0 41.40/10.92 [0 0 0] , 41.40/10.92 41.40/10.92 [1 0 1] [0] 41.40/10.92 [a](x0) = [0 0 0]x0 + [1] 41.40/10.92 [0 1 0] [0] 41.40/10.92 orientation: 41.40/10.92 [1 1 1] [0] [1 0 0] 41.40/10.92 a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(b(x1))) 41.40/10.92 [0 0 0] [1] [0 0 0] 41.40/10.92 41.40/10.92 [1 1 1] [1] [1 0 1] [0] 41.40/10.92 a(a(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(b(a(x1))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [0] 41.40/10.92 41.40/10.92 [1 0 1] [0] [1 0 0] 41.40/10.92 a(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(a(b(b(x1))))) 41.40/10.92 [0 0 0] [0] [0 0 0] 41.40/10.92 41.40/10.92 [1 1 1] [2] [1 1 1] [0] 41.40/10.92 a(a(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(a(b(a(a(x1))))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [1] 41.40/10.92 41.40/10.92 [1 0 1] [0] [1 0 0] [0] 41.40/10.92 a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(a(b(a(b(x1))))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [0] 41.40/10.92 41.40/10.92 [1 1 1] [0] [1 0 1] 41.40/10.92 a(b(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(b(a(b(b(a(x1))))))) 41.40/10.92 [0 0 0] [0] [0 0 0] 41.40/10.92 41.40/10.92 [1 0 1] [0] [1 0 0] 41.40/10.92 a(b(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(b(a(b(b(b(x1))))))) 41.40/10.92 [0 0 0] [0] [0 0 0] 41.40/10.92 41.40/10.92 [1 1 1] [3] [1 1 1] [2] 41.40/10.92 a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(b(a(a(a(x1))))))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [1] 41.40/10.92 41.40/10.92 [1 0 1] [1] [1 0 0] [0] 41.40/10.92 a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(b(a(a(b(x1))))))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [1] 41.40/10.92 41.40/10.92 [1 1 1] [0] [1 0 1] [0] 41.40/10.92 a(a(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(b(a(b(a(b(a(x1))))))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [0] 41.40/10.92 41.40/10.92 [1 0 1] [0] [1 0 0] [0] 41.40/10.92 a(a(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(b(a(b(a(b(b(x1))))))))) 41.40/10.92 [0 0 0] [1] [0 0 0] [0] 41.40/10.92 41.40/10.92 [1 1 1] [1] [1 1 1] 41.40/10.92 a(b(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(a(b(a(b(b(a(a(x1))))))))) 41.40/10.92 [0 0 0] [0] [0 0 0] 41.40/10.92 41.40/10.92 [1 0 1] [0] [1 0 0] 41.40/10.92 a(b(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(b(b(a(b(b(a(b(x1))))))))) 41.40/10.92 [0 0 0] [0] [0 0 0] 41.40/10.92 41.40/10.92 [1 1 1] [0] [1 0 1] 41.40/10.94 a(b(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(a(b(a(b(b(b(a(x1))))))))) 41.40/10.94 [0 0 0] [0] [0 0 0] 41.40/10.94 41.40/10.94 [1 0 1] [0] [1 0 0] 41.40/10.94 a(b(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(b(b(a(b(b(b(b(x1))))))))) 41.40/10.94 [0 0 0] [0] [0 0 0] 41.40/10.94 problem: 41.40/10.94 a(a(x1)) -> b(a(b(x1))) 41.40/10.94 a(b(a(x1))) -> b(b(a(b(b(x1))))) 41.40/10.94 a(a(b(a(x1)))) -> a(b(b(a(b(a(b(x1))))))) 41.40/10.94 a(b(a(a(x1)))) -> b(a(b(a(b(b(a(x1))))))) 41.40/10.94 a(b(b(a(x1)))) -> b(b(b(a(b(b(b(x1))))))) 41.40/10.94 a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(b(a(x1))))))))) 41.40/10.94 a(a(b(b(a(x1))))) -> a(b(b(b(a(b(a(b(b(x1))))))))) 41.40/10.94 a(b(a(b(a(x1))))) -> b(a(b(b(a(b(b(a(b(x1))))))))) 41.40/10.94 a(b(b(a(a(x1))))) -> b(b(a(b(a(b(b(b(a(x1))))))))) 41.40/10.94 a(b(b(b(a(x1))))) -> b(b(b(b(a(b(b(b(b(x1))))))))) 41.40/10.94 Matrix Interpretation Processor: dim=3 41.40/10.94 41.40/10.94 interpretation: 41.40/10.94 [1 0 0] [0] 41.40/10.94 [b](x0) = [0 0 0]x0 + [1] 41.40/10.94 [0 0 0] [0], 41.40/10.94 41.40/10.94 [1 0 1] [0] 41.40/10.94 [a](x0) = [0 0 0]x0 + [1] 41.40/10.94 [0 1 0] [0] 41.40/10.94 orientation: 41.40/10.94 [1 1 1] [0] [1 0 0] [0] 41.40/10.94 a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(x1))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 41.40/10.94 [1 0 1] [0] [1 0 0] [0] 41.40/10.94 a(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(a(b(b(x1))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 41.40/10.94 [1 0 1] [1] [1 0 0] [0] 41.40/10.94 a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(a(b(a(b(x1))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [1] 41.40/10.94 41.40/10.94 [1 1 1] [0] [1 0 1] [0] 41.40/10.94 a(b(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(a(b(b(a(x1))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 41.40/10.94 [1 0 1] [0] [1 0 0] [0] 41.40/10.94 a(b(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(a(b(b(b(x1))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 41.40/10.94 [1 1 1] [1] [1 0 1] [0] 41.40/10.94 a(a(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(b(a(b(a(b(a(x1))))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [1] 41.40/10.94 41.40/10.94 [1 0 1] [1] [1 0 0] [0] 41.40/10.94 a(a(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(b(a(b(a(b(b(x1))))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [1] 41.40/10.94 41.40/10.94 [1 0 1] [0] [1 0 0] [0] 41.40/10.94 a(b(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(b(a(b(b(a(b(x1))))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 41.40/10.94 [1 1 1] [0] [1 0 1] [0] 41.40/10.94 a(b(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(a(b(a(b(b(b(a(x1))))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 41.40/10.94 [1 0 1] [0] [1 0 0] [0] 41.40/10.94 a(b(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(b(a(b(b(b(b(x1))))))))) 41.40/10.94 [0 0 0] [1] [0 0 0] [0] 41.40/10.94 problem: 41.40/10.94 a(a(x1)) -> b(a(b(x1))) 41.40/10.94 a(b(a(x1))) -> b(b(a(b(b(x1))))) 41.40/10.94 a(b(a(a(x1)))) -> b(a(b(a(b(b(a(x1))))))) 41.40/10.94 a(b(b(a(x1)))) -> b(b(b(a(b(b(b(x1))))))) 41.40/10.94 a(b(a(b(a(x1))))) -> b(a(b(b(a(b(b(a(b(x1))))))))) 41.40/10.94 a(b(b(a(a(x1))))) -> b(b(a(b(a(b(b(b(a(x1))))))))) 41.40/10.94 a(b(b(b(a(x1))))) -> b(b(b(b(a(b(b(b(b(x1))))))))) 41.40/10.94 String Reversal Processor: 41.40/10.94 a(a(x1)) -> b(a(b(x1))) 41.40/10.94 a(b(a(x1))) -> b(b(a(b(b(x1))))) 41.40/10.94 a(a(b(a(x1)))) -> a(b(b(a(b(a(b(x1))))))) 41.40/10.94 a(b(b(a(x1)))) -> b(b(b(a(b(b(b(x1))))))) 41.40/10.94 a(b(a(b(a(x1))))) -> b(a(b(b(a(b(b(a(b(x1))))))))) 41.40/10.94 a(a(b(b(a(x1))))) -> a(b(b(b(a(b(a(b(b(x1))))))))) 41.40/10.94 a(b(b(b(a(x1))))) -> b(b(b(b(a(b(b(b(b(x1))))))))) 41.40/10.94 Bounds Processor: 41.40/10.94 bound: 1 41.40/10.94 enrichment: match 41.40/10.94 automaton: 41.40/10.94 final states: {29,24,18,13,9,5,1} 41.40/10.94 transitions: 41.40/10.94 b1(65) -> 66* 41.40/10.94 b1(60) -> 61* 41.40/10.94 b1(35) -> 36* 41.40/10.94 b1(137) -> 138* 41.40/10.94 b1(132) -> 133* 41.40/10.94 b1(92) -> 93* 41.40/10.94 b1(87) -> 88* 41.40/10.94 b1(57) -> 58* 41.40/10.94 b1(144) -> 145* 41.40/10.94 b1(129) -> 130* 41.40/10.94 b1(119) -> 120* 41.40/10.94 b1(114) -> 115* 41.40/10.94 b1(89) -> 90* 41.40/10.94 b1(84) -> 85* 41.40/10.94 b1(64) -> 65* 41.40/10.94 b1(59) -> 60* 41.40/10.94 b1(54) -> 55* 41.40/10.94 b1(39) -> 40* 41.40/10.94 b1(161) -> 162* 41.40/10.94 b1(146) -> 147* 41.40/10.94 b1(121) -> 122* 41.40/10.94 b1(116) -> 117* 41.40/10.94 b1(91) -> 92* 41.40/10.94 b1(81) -> 82* 41.40/10.94 b1(61) -> 62* 41.40/10.94 b1(56) -> 57* 41.40/10.94 b1(36) -> 37* 41.40/10.94 b1(148) -> 149* 41.40/10.94 b1(143) -> 144* 41.40/10.94 b1(133) -> 134* 41.40/10.94 b1(118) -> 119* 41.40/10.94 b1(113) -> 114* 41.40/10.94 b1(93) -> 94* 41.40/10.94 b1(88) -> 89* 41.40/10.94 b1(83) -> 84* 41.40/10.94 b1(63) -> 64* 41.40/10.94 b1(53) -> 54* 41.40/10.94 b1(38) -> 39* 41.40/10.94 b1(145) -> 146* 41.40/10.94 b1(135) -> 136* 41.40/10.94 b1(130) -> 131* 41.40/10.94 b1(120) -> 121* 41.40/10.94 b1(115) -> 116* 41.40/10.94 b1(85) -> 86* 41.40/10.94 a1(55) -> 56* 41.40/10.94 a1(157) -> 158* 41.40/10.94 a1(147) -> 148* 41.40/10.94 a1(117) -> 118* 41.40/10.94 a1(82) -> 83* 41.40/10.94 a1(62) -> 63* 41.40/10.94 a1(37) -> 38* 41.40/10.94 a1(136) -> 137* 41.40/10.94 a1(131) -> 132* 41.40/10.94 a1(90) -> 91* 41.40/10.94 f20() -> 2* 41.40/10.94 b0(25) -> 26* 41.40/10.94 b0(20) -> 21* 41.40/10.94 b0(15) -> 16* 41.40/10.94 b0(10) -> 11* 41.40/10.94 b0(32) -> 33* 41.40/10.94 b0(27) -> 28* 41.40/10.94 b0(17) -> 13* 41.40/10.94 b0(7) -> 8* 41.40/10.94 b0(2) -> 3* 41.40/10.94 b0(34) -> 29* 41.40/10.94 b0(14) -> 30* 41.40/10.94 b0(4) -> 1* 41.40/10.94 b0(31) -> 32* 41.40/10.94 b0(26) -> 27* 41.40/10.94 b0(21) -> 22* 41.40/10.94 b0(16) -> 17* 41.40/10.94 b0(11) -> 12* 41.40/10.94 b0(6) -> 14* 41.40/10.94 b0(1) -> 19* 41.40/10.94 b0(33) -> 34* 41.40/10.94 b0(23) -> 18* 41.40/10.94 b0(8) -> 5* 41.40/10.94 b0(3) -> 6* 41.40/10.94 a0(30) -> 31* 41.40/10.94 a0(22) -> 23* 41.40/10.94 a0(12) -> 9* 41.40/10.94 a0(19) -> 20* 41.40/10.94 a0(14) -> 15* 41.40/10.94 a0(6) -> 7* 41.40/10.94 a0(1) -> 10* 41.40/10.94 a0(28) -> 24* 41.40/10.94 a0(8) -> 25* 41.40/10.94 a0(3) -> 4* 41.40/10.94 1 -> 59* 41.40/10.94 3 -> 53* 41.40/10.94 5 -> 4* 41.40/10.94 6 -> 35* 41.40/10.94 8 -> 113* 41.40/10.94 11 -> 4,7 41.40/10.94 18 -> 4,10 41.40/10.94 19 -> 87* 41.40/10.94 21 -> 4,7,56,15 41.40/10.94 22 -> 143* 41.40/10.94 37 -> 129* 41.40/10.94 40 -> 25* 41.40/10.94 55 -> 81* 41.40/10.94 58 -> 10* 41.40/10.94 62 -> 135* 41.40/10.94 66 -> 20,10,25,9 41.40/10.94 86 -> 20* 41.40/10.94 90 -> 161* 41.40/10.94 94 -> 10,25,23 41.40/10.94 122 -> 24* 41.40/10.94 134 -> 56* 41.40/10.94 138 -> 83* 41.40/10.94 146 -> 157* 41.40/10.94 149 -> 63* 41.40/10.94 158 -> 63* 41.40/10.94 162 -> 136* 41.40/10.94 problem: 41.40/10.94 41.40/10.94 Qed 41.40/10.94 EOF