63.29/16.71 YES 63.29/16.72 63.29/16.72 Problem: 63.29/16.72 b(a(b(x1))) -> b(a(a(a(b(x1))))) 63.29/16.72 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 63.29/16.72 b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1) 63.29/16.72 b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) 63.29/16.72 b(a(a(b(b(x1))))) -> b(x1) 63.29/16.72 b(b(a(a(b(x1))))) -> b(x1) 63.29/16.72 b(a(a(a(b(a(b(x1))))))) -> b(x1) 63.29/16.72 b(a(b(a(a(a(b(x1))))))) -> b(x1) 63.29/16.72 63.29/16.72 Proof: 63.29/16.72 Matrix Interpretation Processor: dim=3 63.29/16.72 63.29/16.72 interpretation: 63.29/16.72 [1 0 0] 63.29/16.72 [a](x0) = [0 0 0]x0 63.29/16.72 [0 1 0] , 63.29/16.72 63.29/16.72 [1 0 1] [0] 63.29/16.72 [b](x0) = [0 0 0]x0 + [1] 63.29/16.72 [0 0 0] [0] 63.29/16.72 orientation: 63.29/16.72 [1 0 1] [1] [1 0 1] [0] 63.29/16.72 b(a(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(a(b(x1))))) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [0] [1 0 1] [0] 63.29/16.72 b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [0] [1 0 1] [0] 63.29/16.72 b(a(a(a(b(a(a(a(b(x1))))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [0] [1 0 1] [0] 63.29/16.72 b(a(a(a(b(b(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(a(a(a(b(x1))))))) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [0] [1 0 1] [0] 63.29/16.72 b(a(a(b(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [0] [1 0 1] [0] 63.29/16.72 b(b(a(a(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [1] [1 0 1] [0] 63.29/16.72 b(a(a(a(b(a(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 63.29/16.72 [1 0 1] [1] [1 0 1] [0] 63.29/16.72 b(a(b(a(a(a(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 63.29/16.72 [0 0 0] [0] [0 0 0] [0] 63.29/16.72 problem: 63.29/16.72 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 63.29/16.72 b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1) 63.29/16.72 b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) 63.29/16.72 b(a(a(b(b(x1))))) -> b(x1) 63.29/16.72 b(b(a(a(b(x1))))) -> b(x1) 63.29/16.72 String Reversal Processor: 63.29/16.72 b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) 63.29/16.72 b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1) 63.29/16.72 b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) 63.29/16.72 b(b(a(a(b(x1))))) -> b(x1) 63.29/16.72 b(a(a(b(b(x1))))) -> b(x1) 63.29/16.72 Matrix Interpretation Processor: dim=3 63.29/16.72 63.29/16.72 interpretation: 63.29/16.72 [1 0 0] 63.29/16.72 [a](x0) = [0 0 1]x0 63.29/16.72 [0 1 0] , 63.29/16.72 63.29/16.72 [1 1 0] [0] 63.29/16.72 [b](x0) = [0 0 0]x0 + [0] 63.29/16.72 [0 0 0] [1] 63.29/16.72 orientation: 63.29/16.72 [1 1 0] [1] [1 1 0] [1] 63.29/16.72 b(a(a(b(a(a(a(b(x1)))))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) 63.29/16.72 [0 0 0] [1] [0 0 0] [1] 63.29/16.72 63.29/16.72 [1 1 0] [2] [1 1 0] [0] 63.29/16.72 b(a(a(a(b(a(a(a(b(x1))))))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(x1) 63.29/16.72 [0 0 0] [1] [0 0 0] [1] 63.29/16.72 63.29/16.72 [1 1 0] [1] [1 1 0] [1] 63.29/16.72 b(b(b(a(a(a(b(x1))))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(a(a(b(b(b(x1))))))) 63.29/16.72 [0 0 0] [1] [0 0 0] [1] 63.29/16.72 63.29/16.72 [1 1 0] [0] [1 1 0] [0] 64.09/16.73 b(b(a(a(b(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(x1) 64.09/16.73 [0 0 0] [1] [0 0 0] [1] 64.09/16.73 64.09/16.73 [1 1 0] [0] [1 1 0] [0] 64.09/16.73 b(a(a(b(b(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(x1) 64.09/16.73 [0 0 0] [1] [0 0 0] [1] 64.09/16.73 problem: 64.09/16.73 b(a(a(b(a(a(a(b(x1)))))))) -> b(b(a(a(a(b(a(a(b(a(a(b(x1)))))))))))) 64.09/16.73 b(b(b(a(a(a(b(x1))))))) -> b(a(a(a(b(b(b(x1))))))) 64.09/16.73 b(b(a(a(b(x1))))) -> b(x1) 64.09/16.73 b(a(a(b(b(x1))))) -> b(x1) 64.09/16.73 String Reversal Processor: 64.09/16.73 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 64.09/16.73 b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) 64.09/16.73 b(a(a(b(b(x1))))) -> b(x1) 64.09/16.73 b(b(a(a(b(x1))))) -> b(x1) 64.09/16.73 Matrix Interpretation Processor: dim=3 64.09/16.73 64.09/16.73 interpretation: 64.09/16.73 [1 1 0] 64.09/16.73 [a](x0) = [0 0 1]x0 64.09/16.73 [1 0 0] , 64.09/16.73 64.09/16.73 [1 0 0] [0] 64.09/16.73 [b](x0) = [0 0 0]x0 + [1] 64.09/16.73 [0 0 0] [0] 64.09/16.73 orientation: 64.09/16.73 [2 0 0] [3] [2 0 0] [3] 64.09/16.73 b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 64.09/16.73 [0 0 0] [0] [0 0 0] [0] 64.09/16.73 64.09/16.73 [2 0 0] [1] [2 0 0] [1] 64.09/16.73 b(a(a(a(b(b(b(x1))))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(a(a(a(b(x1))))))) 64.09/16.73 [0 0 0] [0] [0 0 0] [0] 64.09/16.73 64.09/16.73 [1 0 0] [1] [1 0 0] [0] 64.09/16.73 b(a(a(b(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 64.09/16.73 [0 0 0] [0] [0 0 0] [0] 64.09/16.73 64.09/16.73 [1 0 0] [1] [1 0 0] [0] 64.09/16.73 b(b(a(a(b(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 64.09/16.73 [0 0 0] [0] [0 0 0] [0] 64.09/16.73 problem: 64.09/16.73 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 64.09/16.73 b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) 64.09/16.73 Matrix Interpretation Processor: dim=4 64.09/16.73 64.09/16.73 interpretation: 64.09/16.73 [1 0 0 0] [0] 64.09/16.73 [0 0 0 1] [0] 64.09/16.73 [a](x0) = [0 0 0 1]x0 + [1] 64.09/16.73 [0 1 0 0] [0], 64.09/16.73 64.09/16.73 [1 1 0 0] 64.09/16.73 [0 0 0 0] 64.09/16.73 [b](x0) = [0 0 0 0]x0 64.09/16.73 [0 1 1 1] 64.09/16.73 orientation: 64.09/16.73 [1 2 1 1] [1] [1 2 1 1] [0] 64.09/16.73 [0 0 0 0] [0] [0 0 0 0] [0] 64.09/16.73 b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) 64.09/16.73 [0 2 2 2] [3] [0 2 2 2] [3] 64.09/16.73 64.09/16.73 [1 2 1 1] [0] [1 2 1 1] [0] 64.09/16.73 [0 0 0 0] [0] [0 0 0 0] [0] 64.09/16.73 b(a(a(a(b(b(b(x1))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(b(b(a(a(a(b(x1))))))) 64.09/16.73 [0 2 2 2] [1] [0 2 2 2] [1] 64.09/16.73 problem: 64.09/16.73 b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) 64.09/16.73 KBO Processor: 64.09/16.73 weight function: 64.09/16.73 w0 = 1 64.09/16.73 w(a) = w(b) = 1 64.09/16.73 precedence: 64.09/16.73 a > b 64.09/16.73 problem: 64.09/16.73 64.09/16.73 Qed 64.10/16.73 EOF