29.65/7.94 YES 29.65/7.95 29.65/7.95 Problem: 29.65/7.95 strict: 29.65/7.95 a(b(b(x1))) -> c(b(c(x1))) 29.65/7.95 c(a(b(x1))) -> a(c(b(x1))) 29.65/7.95 c(c(a(x1))) -> c(b(b(x1))) 29.65/7.95 weak: 29.65/7.95 b(c(c(x1))) -> b(a(c(x1))) 29.65/7.95 a(c(b(x1))) -> c(b(a(x1))) 29.65/7.95 c(c(b(x1))) -> c(a(c(x1))) 29.65/7.95 29.65/7.95 Proof: 29.65/7.95 String Reversal Processor: 29.65/7.95 strict: 29.65/7.95 b(b(a(x1))) -> c(b(c(x1))) 29.65/7.95 b(a(c(x1))) -> b(c(a(x1))) 29.65/7.95 a(c(c(x1))) -> b(b(c(x1))) 29.65/7.95 weak: 29.65/7.95 c(c(b(x1))) -> c(a(b(x1))) 29.65/7.95 b(c(a(x1))) -> a(b(c(x1))) 29.65/7.95 b(c(c(x1))) -> c(a(c(x1))) 29.65/7.95 Matrix Interpretation Processor: dim=2 29.65/7.95 29.65/7.95 interpretation: 29.65/7.95 [1 0] [1] 29.65/7.95 [c](x0) = [0 0]x0 + [0], 29.65/7.95 29.65/7.95 [1 0] [0] 29.65/7.95 [a](x0) = [0 0]x0 + [1], 29.65/7.95 29.65/7.95 [1 1] [0] 29.65/7.95 [b](x0) = [0 0]x0 + [1] 29.65/7.95 orientation: 29.65/7.95 [1 0] [2] [1 0] [2] 29.65/7.95 b(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(b(c(x1))) 29.65/7.95 29.65/7.95 [1 0] [2] [1 0] [1] 29.65/7.95 b(a(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(a(x1))) 29.65/7.95 29.65/7.95 [1 0] [2] [1 0] [2] 29.65/7.95 a(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(b(c(x1))) 29.65/7.95 29.65/7.95 [1 1] [2] [1 1] [1] 29.65/7.95 c(c(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(a(b(x1))) 29.65/7.95 29.65/7.95 [1 0] [1] [1 0] [1] 29.65/7.95 b(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(b(c(x1))) 29.65/7.95 29.65/7.95 [1 0] [2] [1 0] [2] 29.65/7.95 b(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = c(a(c(x1))) 29.65/7.95 problem: 29.65/7.95 strict: 29.65/7.95 b(b(a(x1))) -> c(b(c(x1))) 29.65/7.95 a(c(c(x1))) -> b(b(c(x1))) 29.65/7.95 weak: 29.65/7.95 b(c(a(x1))) -> a(b(c(x1))) 29.65/7.95 b(c(c(x1))) -> c(a(c(x1))) 29.65/7.95 String Reversal Processor: 29.65/7.95 strict: 29.65/7.95 a(b(b(x1))) -> c(b(c(x1))) 29.65/7.95 c(c(a(x1))) -> c(b(b(x1))) 29.65/7.95 weak: 29.65/7.95 a(c(b(x1))) -> c(b(a(x1))) 29.65/7.95 c(c(b(x1))) -> c(a(c(x1))) 29.65/7.95 Bounds Processor: 29.65/7.95 bound: 1 29.65/7.95 enrichment: match-rt 29.65/7.95 automaton: 29.65/7.95 final states: {3,2,1} 29.65/7.95 transitions: 29.65/7.95 c1(30) -> 31* 29.65/7.95 c1(5) -> 6* 29.65/7.95 c1(7) -> 8* 29.65/7.95 c1(136) -> 137* 29.65/7.95 c1(193) -> 194* 29.65/7.95 c1(78) -> 79* 29.65/7.95 c1(28) -> 29* 29.65/7.95 c1(195) -> 196* 29.65/7.95 c1(120) -> 121* 29.65/7.95 b1(45) -> 46* 29.65/7.95 b1(102) -> 103* 29.65/7.95 b1(62) -> 63* 29.65/7.95 b1(47) -> 48* 29.65/7.95 b1(119) -> 120* 29.65/7.95 b1(44) -> 45* 29.65/7.95 b1(101) -> 102* 29.65/7.95 b1(6) -> 7* 29.65/7.95 a1(172) -> 173* 29.65/7.95 a1(162) -> 163* 29.65/7.95 a1(154) -> 155* 29.65/7.95 a1(134) -> 135* 29.65/7.95 a1(79) -> 80* 29.65/7.95 a1(146) -> 147* 29.65/7.95 a1(76) -> 77* 29.65/7.95 a1(213) -> 214* 29.65/7.95 a1(128) -> 129* 29.65/7.95 a1(118) -> 119* 29.65/7.95 a1(160) -> 161* 29.65/7.95 a0(2) -> 1* 29.65/7.95 a0(1) -> 1* 29.65/7.95 a0(3) -> 1* 29.65/7.95 b0(2) -> 2* 29.65/7.95 b0(1) -> 2* 29.65/7.95 b0(3) -> 2* 29.65/7.95 c0(2) -> 3* 29.65/7.95 c0(1) -> 3* 29.65/7.95 c0(3) -> 3* 29.65/7.95 1 -> 134,47,28 29.65/7.95 2 -> 128,44,5 29.65/7.95 3 -> 1,62,30 29.65/7.95 6 -> 78,76 29.65/7.95 8 -> 173,161,135,163,129,119,1 29.65/7.95 29 -> 3,6 29.65/7.95 31 -> 29,79,6 29.65/7.95 44 -> 162* 29.65/7.95 45 -> 136,118 29.65/7.95 46 -> 30* 29.65/7.95 47 -> 160* 29.65/7.95 48 -> 45* 29.65/7.95 62 -> 154* 29.65/7.95 63 -> 45* 29.65/7.95 76 -> 101* 29.65/7.95 77 -> 6* 29.65/7.95 79 -> 3,31 29.65/7.95 80 -> 28* 29.65/7.95 101 -> 213* 29.65/7.95 102 -> 193,146 29.65/7.95 103 -> 78* 29.65/7.95 119 -> 195,172 29.65/7.95 121 -> 214,173,161,155,135,1,80,77 29.65/7.95 129 -> 119* 29.65/7.95 135 -> 119* 29.65/7.95 137 -> 76* 29.65/7.95 147 -> 119* 29.65/7.95 155 -> 119* 29.65/7.95 161 -> 119* 29.65/7.95 163 -> 119* 29.65/7.95 173 -> 119* 29.65/7.95 194 -> 76* 29.65/7.95 196 -> 76* 29.65/7.95 214 -> 119* 29.65/7.95 problem: 29.65/7.95 strict: 29.65/7.95 c(c(a(x1))) -> c(b(b(x1))) 29.65/7.95 weak: 29.65/7.95 a(c(b(x1))) -> c(b(a(x1))) 29.65/7.95 c(c(b(x1))) -> c(a(c(x1))) 29.65/7.95 String Reversal Processor: 29.65/7.95 strict: 29.65/7.95 a(c(c(x1))) -> b(b(c(x1))) 29.65/7.95 weak: 29.65/7.95 b(c(a(x1))) -> a(b(c(x1))) 29.65/7.95 b(c(c(x1))) -> c(a(c(x1))) 29.65/7.95 Arctic Interpretation Processor: 29.65/7.95 dimension: 1 29.65/7.95 interpretation: 29.65/7.95 [c](x0) = 8x0, 29.65/7.95 29.65/7.95 [a](x0) = 4x0, 29.65/7.95 29.65/7.95 [b](x0) = 6x0 29.65/7.95 orientation: 29.65/7.95 a(c(c(x1))) = 20x1 >= 20x1 = b(b(c(x1))) 29.65/7.95 29.65/7.95 b(c(a(x1))) = 18x1 >= 18x1 = a(b(c(x1))) 29.65/7.95 29.65/7.95 b(c(c(x1))) = 22x1 >= 20x1 = c(a(c(x1))) 29.65/7.95 problem: 29.65/7.95 strict: 29.65/7.95 a(c(c(x1))) -> b(b(c(x1))) 29.65/7.95 weak: 29.65/7.95 b(c(a(x1))) -> a(b(c(x1))) 29.65/7.95 RT Transformation Processor: 29.65/7.95 a(c(c(x1))) -> b(b(c(x1))) 29.65/7.95 b(c(a(x1))) -> a(b(c(x1))) 29.65/7.95 Matrix Interpretation Processor: dim=3 29.65/7.95 29.65/7.95 interpretation: 29.65/7.95 [1 0 0] [0] 29.65/7.95 [c](x0) = [0 0 1]x0 + [0] 29.65/7.95 [0 1 0] [1], 29.65/7.95 29.65/7.95 [1 0 0] [1] 29.65/7.95 [a](x0) = [1 1 0]x0 + [0] 29.65/7.95 [1 0 0] [0], 29.65/7.95 29.65/7.95 [1 0 0] 29.65/7.95 [b](x0) = [0 0 1]x0 29.65/7.95 [1 0 0] 29.65/7.95 orientation: 29.65/7.95 [1 0 0] [1] [1 0 0] 29.65/7.95 a(c(c(x1))) = [1 1 0]x1 + [1] >= [1 0 0]x1 = b(b(c(x1))) 29.65/7.95 [1 0 0] [0] [1 0 0] 29.65/7.95 29.65/7.95 [1 0 0] [1] [1 0 0] [1] 29.65/7.95 b(c(a(x1))) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = a(b(c(x1))) 29.65/7.95 [1 0 0] [1] [1 0 0] [0] 29.65/7.95 problem: 29.65/7.95 b(c(a(x1))) -> a(b(c(x1))) 29.65/7.95 Matrix Interpretation Processor: dim=3 29.65/7.95 29.65/7.95 interpretation: 29.65/7.95 [1 0 1] [0] 29.65/7.95 [c](x0) = [1 0 0]x0 + [1] 29.65/7.95 [0 1 0] [0], 29.65/7.95 29.65/7.95 [1 1 0] [0] 29.65/7.95 [a](x0) = [0 0 0]x0 + [0] 29.65/7.95 [0 0 1] [1], 29.65/7.95 29.65/7.95 [1 0 1] 29.65/7.95 [b](x0) = [0 0 0]x0 29.65/7.95 [1 0 0] 29.65/7.95 orientation: 29.65/7.95 [1 1 1] [1] [1 1 1] [0] 29.65/7.95 b(c(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(c(x1))) 29.65/7.95 [1 1 1] [1] [1 0 1] [1] 29.65/7.95 problem: 29.65/7.95 29.65/7.95 Qed 29.98/7.96 EOF