29.75/7.89 YES 29.75/7.90 29.75/7.90 Problem: 29.75/7.90 strict: 29.75/7.90 a(c(a(x1))) -> a(c(b(x1))) 29.75/7.90 b(b(c(x1))) -> b(c(c(x1))) 29.75/7.90 c(c(b(x1))) -> c(a(b(x1))) 29.75/7.90 b(a(a(x1))) -> a(b(a(x1))) 29.75/7.90 b(a(c(x1))) -> a(b(a(x1))) 29.75/7.90 a(c(a(x1))) -> b(c(c(x1))) 29.75/7.90 weak: 29.75/7.90 b(c(a(x1))) -> b(a(a(x1))) 29.75/7.90 29.75/7.90 Proof: 29.75/7.90 Matrix Interpretation Processor: dim=2 29.75/7.90 29.75/7.90 interpretation: 29.75/7.90 [1 0] 29.75/7.90 [b](x0) = [0 0]x0, 29.75/7.90 29.75/7.90 [0] 29.75/7.90 [c](x0) = x0 + [1], 29.75/7.90 29.75/7.90 [1 2] 29.75/7.90 [a](x0) = [0 0]x0 29.75/7.90 orientation: 29.75/7.90 [1 2] [2] [1 0] [2] 29.75/7.90 a(c(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c(b(x1))) 29.75/7.90 29.75/7.90 [1 0] [1 0] 29.75/7.90 b(b(c(x1))) = [0 0]x1 >= [0 0]x1 = b(c(c(x1))) 29.75/7.90 29.75/7.90 [1 0] [0] [1 0] [0] 29.75/7.90 c(c(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [1] = c(a(b(x1))) 29.75/7.90 29.75/7.90 [1 2] [1 2] 29.75/7.90 b(a(a(x1))) = [0 0]x1 >= [0 0]x1 = a(b(a(x1))) 29.75/7.90 29.75/7.90 [1 2] [2] [1 2] 29.75/7.90 b(a(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 = a(b(a(x1))) 29.75/7.90 29.75/7.90 [1 2] [2] [1 0] 29.75/7.90 a(c(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 = b(c(c(x1))) 29.75/7.90 29.75/7.90 [1 2] [1 2] 29.75/7.90 b(c(a(x1))) = [0 0]x1 >= [0 0]x1 = b(a(a(x1))) 29.75/7.90 problem: 29.75/7.90 strict: 29.75/7.90 a(c(a(x1))) -> a(c(b(x1))) 29.75/7.90 b(b(c(x1))) -> b(c(c(x1))) 29.75/7.90 c(c(b(x1))) -> c(a(b(x1))) 29.75/7.90 b(a(a(x1))) -> a(b(a(x1))) 29.75/7.90 weak: 29.75/7.90 b(c(a(x1))) -> b(a(a(x1))) 29.75/7.90 String Reversal Processor: 29.75/7.90 strict: 29.75/7.90 a(c(a(x1))) -> b(c(a(x1))) 29.75/7.90 c(b(b(x1))) -> c(c(b(x1))) 29.75/7.90 b(c(c(x1))) -> b(a(c(x1))) 29.75/7.90 a(a(b(x1))) -> a(b(a(x1))) 29.75/7.90 weak: 29.75/7.90 a(c(b(x1))) -> a(a(b(x1))) 29.75/7.90 Matrix Interpretation Processor: dim=2 29.75/7.90 29.75/7.90 interpretation: 29.75/7.90 [1 0] [0] 29.75/7.90 [b](x0) = [0 0]x0 + [1], 29.75/7.90 29.75/7.90 [1 2] 29.75/7.90 [c](x0) = [0 0]x0, 29.75/7.90 29.75/7.90 [1 0] [0] 29.75/7.90 [a](x0) = [0 0]x0 + [1] 29.75/7.90 orientation: 29.75/7.90 [1 0] [2] [1 0] [2] 29.75/7.90 a(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(a(x1))) 29.75/7.90 29.75/7.90 [1 0] [2] [1 0] [2] 29.75/7.90 c(b(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(c(b(x1))) 29.75/7.90 29.75/7.90 [1 2] [0] [1 2] [0] 29.75/7.90 b(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1))) 29.75/7.90 29.75/7.90 [1 0] [0] [1 0] [0] 29.75/7.90 a(a(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(b(a(x1))) 29.75/7.90 29.75/7.90 [1 0] [2] [1 0] [0] 29.75/7.90 a(c(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(a(b(x1))) 29.75/7.90 problem: 29.75/7.90 strict: 29.75/7.90 a(c(a(x1))) -> b(c(a(x1))) 29.75/7.90 c(b(b(x1))) -> c(c(b(x1))) 29.75/7.90 b(c(c(x1))) -> b(a(c(x1))) 29.75/7.90 a(a(b(x1))) -> a(b(a(x1))) 29.75/7.90 weak: 29.75/7.90 29.75/7.90 Matrix Interpretation Processor: dim=2 29.75/7.90 29.75/7.90 interpretation: 29.75/7.90 [1 0] [1] 29.75/7.90 [b](x0) = [1 0]x0 + [0], 29.75/7.90 29.75/7.90 [1 1] [0] 29.75/7.90 [c](x0) = [0 0]x0 + [2], 29.75/7.90 29.75/7.90 [1 0] [1] 29.75/7.90 [a](x0) = [1 0]x0 + [0] 29.75/7.90 orientation: 29.75/7.90 [2 0] [2] [2 0] [2] 29.75/7.90 a(c(a(x1))) = [2 0]x1 + [1] >= [2 0]x1 + [1] = b(c(a(x1))) 29.75/7.90 29.75/7.90 [2 0] [3] [2 0] [3] 29.75/7.90 c(b(b(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = c(c(b(x1))) 29.75/7.90 29.75/7.90 [1 1] [3] [1 1] [2] 29.75/7.90 b(c(c(x1))) = [1 1]x1 + [2] >= [1 1]x1 + [1] = b(a(c(x1))) 29.75/7.90 29.75/7.90 [1 0] [3] [1 0] [3] 29.75/7.90 a(a(b(x1))) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(b(a(x1))) 29.75/7.90 problem: 29.75/7.90 strict: 29.75/7.90 a(c(a(x1))) -> b(c(a(x1))) 29.75/7.90 c(b(b(x1))) -> c(c(b(x1))) 29.75/7.90 a(a(b(x1))) -> a(b(a(x1))) 29.75/7.90 weak: 29.75/7.90 29.75/7.90 String Reversal Processor: 29.75/7.90 strict: 29.75/7.90 a(c(a(x1))) -> a(c(b(x1))) 29.75/7.90 b(b(c(x1))) -> b(c(c(x1))) 29.75/7.90 b(a(a(x1))) -> a(b(a(x1))) 29.75/7.90 weak: 29.75/7.90 29.75/7.90 Arctic Interpretation Processor: 29.75/7.90 dimension: 1 29.75/7.90 interpretation: 29.75/7.90 [b](x0) = 4x0, 29.75/7.90 29.75/7.90 [c](x0) = x0, 29.75/7.90 29.75/7.90 [a](x0) = 8x0 29.75/7.90 orientation: 29.75/7.90 a(c(a(x1))) = 16x1 >= 12x1 = a(c(b(x1))) 29.75/7.90 29.75/7.90 b(b(c(x1))) = 8x1 >= 4x1 = b(c(c(x1))) 29.75/7.90 29.75/7.90 b(a(a(x1))) = 20x1 >= 20x1 = a(b(a(x1))) 29.75/7.90 problem: 29.75/7.90 strict: 29.75/7.90 b(a(a(x1))) -> a(b(a(x1))) 29.75/7.90 weak: 29.75/7.90 29.75/7.90 RT Transformation Processor: 29.75/7.90 b(a(a(x1))) -> a(b(a(x1))) 29.75/7.90 Matrix Interpretation Processor: dim=3 29.75/7.90 29.75/7.90 interpretation: 29.75/7.90 [1 0 1] 29.75/7.90 [b](x0) = [0 1 0]x0 29.75/7.90 [0 0 1] , 29.75/7.90 29.75/7.90 [1 0 0] [0] 29.75/7.90 [a](x0) = [0 0 0]x0 + [1] 29.75/7.90 [0 1 1] [0] 29.75/7.90 orientation: 29.75/7.90 [1 1 1] [1] [1 1 1] [0] 29.75/7.90 b(a(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(x1))) 29.75/7.90 [0 1 1] [1] [0 1 1] [1] 29.75/7.90 problem: 29.75/7.90 29.75/7.90 Qed 29.75/7.91 EOF