2.77/1.16 YES 2.77/1.16 2.77/1.16 Problem: 2.77/1.16 a(b(a(x1))) -> b(a(x1)) 2.77/1.16 b(b(b(x1))) -> b(a(b(x1))) 2.77/1.16 a(a(x1)) -> b(b(b(x1))) 2.77/1.16 2.77/1.16 Proof: 2.77/1.16 String Reversal Processor: 2.77/1.16 a(b(a(x1))) -> a(b(x1)) 2.77/1.16 b(b(b(x1))) -> b(a(b(x1))) 2.77/1.16 a(a(x1)) -> b(b(b(x1))) 2.77/1.16 Matrix Interpretation Processor: dim=2 2.77/1.16 2.77/1.16 interpretation: 2.77/1.16 [1 0] 2.77/1.16 [b](x0) = [0 0]x0, 2.77/1.16 2.77/1.16 [1 2] [0] 2.77/1.16 [a](x0) = [2 0]x0 + [2] 2.77/1.16 orientation: 2.77/1.16 [1 2] [0] [1 0] [0] 2.77/1.16 a(b(a(x1))) = [2 4]x1 + [2] >= [2 0]x1 + [2] = a(b(x1)) 2.77/1.16 2.77/1.16 [1 0] [1 0] 2.77/1.16 b(b(b(x1))) = [0 0]x1 >= [0 0]x1 = b(a(b(x1))) 2.77/1.16 2.77/1.16 [5 2] [4] [1 0] 2.77/1.16 a(a(x1)) = [2 4]x1 + [2] >= [0 0]x1 = b(b(b(x1))) 2.77/1.16 problem: 2.77/1.16 a(b(a(x1))) -> a(b(x1)) 2.77/1.16 b(b(b(x1))) -> b(a(b(x1))) 2.77/1.16 KBO Processor: 2.77/1.16 weight function: 2.77/1.16 w0 = 1 2.77/1.16 w(b) = w(a) = 1 2.77/1.16 precedence: 2.77/1.16 b > a 2.77/1.16 problem: 2.77/1.16 2.77/1.16 Qed 2.77/1.17 EOF