21.75/5.86 YES 21.75/5.86 21.75/5.86 Problem: 21.75/5.86 strict: 21.75/5.86 c(c(a(x1))) -> c(c(b(x1))) 21.75/5.86 b(b(c(x1))) -> a(a(b(x1))) 21.75/5.86 weak: 21.75/5.86 b(a(b(x1))) -> a(c(b(x1))) 21.75/5.86 c(a(a(x1))) -> b(a(b(x1))) 21.75/5.86 c(c(c(x1))) -> c(a(c(x1))) 21.75/5.86 21.75/5.86 Proof: 21.75/5.86 String Reversal Processor: 21.75/5.86 strict: 21.75/5.86 a(c(c(x1))) -> b(c(c(x1))) 21.75/5.86 c(b(b(x1))) -> b(a(a(x1))) 21.75/5.86 weak: 21.75/5.86 b(a(b(x1))) -> b(c(a(x1))) 21.75/5.86 a(a(c(x1))) -> b(a(b(x1))) 21.75/5.86 c(c(c(x1))) -> c(a(c(x1))) 21.75/5.86 Matrix Interpretation Processor: dim=2 21.75/5.86 21.75/5.86 interpretation: 21.75/5.86 [1 0] 21.75/5.86 [b](x0) = [0 0]x0, 21.75/5.86 21.75/5.86 [1 1] [0] 21.75/5.86 [c](x0) = [1 0]x0 + [1], 21.75/5.86 21.75/5.86 [1 0] 21.75/5.86 [a](x0) = [0 0]x0 21.75/5.86 orientation: 21.75/5.86 [2 1] [1] [2 1] [1] 21.75/5.86 a(c(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(c(c(x1))) 21.75/5.86 21.75/5.86 [1 0] [0] [1 0] 21.75/5.86 c(b(b(x1))) = [1 0]x1 + [1] >= [0 0]x1 = b(a(a(x1))) 21.75/5.86 21.75/5.86 [1 0] [1 0] 21.75/5.86 b(a(b(x1))) = [0 0]x1 >= [0 0]x1 = b(c(a(x1))) 21.75/5.86 21.75/5.86 [1 1] [1 0] 21.75/5.86 a(a(c(x1))) = [0 0]x1 >= [0 0]x1 = b(a(b(x1))) 21.75/5.86 21.75/5.86 [3 2] [2] [1 1] [0] 21.75/5.86 c(c(c(x1))) = [2 1]x1 + [2] >= [1 1]x1 + [1] = c(a(c(x1))) 21.75/5.86 problem: 21.75/5.86 strict: 21.75/5.86 a(c(c(x1))) -> b(c(c(x1))) 21.75/5.86 c(b(b(x1))) -> b(a(a(x1))) 21.75/5.86 weak: 21.75/5.86 b(a(b(x1))) -> b(c(a(x1))) 21.75/5.86 a(a(c(x1))) -> b(a(b(x1))) 21.75/5.86 String Reversal Processor: 21.75/5.86 strict: 21.75/5.86 c(c(a(x1))) -> c(c(b(x1))) 21.75/5.86 b(b(c(x1))) -> a(a(b(x1))) 21.75/5.86 weak: 21.75/5.86 b(a(b(x1))) -> a(c(b(x1))) 21.75/5.86 c(a(a(x1))) -> b(a(b(x1))) 21.75/5.86 Matrix Interpretation Processor: dim=1 21.75/5.86 21.75/5.86 interpretation: 21.75/5.86 [b](x0) = 3x0, 21.75/5.86 21.75/5.86 [c](x0) = 3x0 + 1, 21.75/5.86 21.75/5.86 [a](x0) = 3x0 + 2 21.75/5.86 orientation: 21.75/5.86 c(c(a(x1))) = 27x1 + 22 >= 27x1 + 4 = c(c(b(x1))) 21.75/5.86 21.75/5.86 b(b(c(x1))) = 27x1 + 9 >= 27x1 + 8 = a(a(b(x1))) 21.75/5.86 21.75/5.86 b(a(b(x1))) = 27x1 + 6 >= 27x1 + 5 = a(c(b(x1))) 21.75/5.86 21.75/5.86 c(a(a(x1))) = 27x1 + 25 >= 27x1 + 6 = b(a(b(x1))) 21.75/5.86 problem: 21.75/5.86 strict: 21.75/5.86 21.75/5.86 weak: 21.75/5.86 21.75/5.86 Qed 21.75/5.87 EOF