32.05/8.73 YES 32.05/8.74 32.05/8.74 Problem: 32.05/8.74 a(a(x1)) -> b(x1) 32.05/8.74 a(a(a(x1))) -> a(b(a(x1))) 32.05/8.74 a(b(a(x1))) -> b(b(b(x1))) 32.05/8.74 a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) 32.05/8.74 a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) 32.05/8.74 a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) 32.05/8.74 a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) 32.05/8.74 a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) 32.05/8.74 a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) 32.05/8.74 a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) 32.05/8.74 a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) 32.05/8.74 a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) 32.05/8.74 a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) 32.05/8.74 a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) 32.05/8.74 a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) 32.05/8.74 32.05/8.74 Proof: 32.05/8.74 Matrix Interpretation Processor: dim=3 32.05/8.74 32.05/8.74 interpretation: 32.05/8.74 [1 0 0] [0] 32.05/8.74 [b](x0) = [0 0 0]x0 + [1] 32.05/8.74 [0 0 0] [0], 32.05/8.74 32.05/8.74 [1 0 1] [0] 32.05/8.74 [a](x0) = [0 0 0]x0 + [1] 32.05/8.74 [0 1 0] [0] 32.05/8.74 orientation: 32.05/8.74 [1 1 1] [0] [1 0 0] [0] 32.05/8.74 a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(x1) 32.05/8.74 [0 0 0] [1] [0 0 0] [0] 32.05/8.74 32.05/8.74 [1 1 1] [1] [1 0 1] [0] 32.05/8.74 a(a(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(x1))) 32.05/8.74 [0 0 0] [1] [0 0 0] [1] 32.05/8.74 32.05/8.74 [1 0 1] [0] [1 0 0] [0] 32.05/8.74 a(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(x1))) 32.05/8.74 [0 0 0] [1] [0 0 0] [0] 32.05/8.74 32.05/8.74 [1 1 1] [2] [1 1 1] [1] 32.05/8.74 a(a(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(a(a(x1))))) 32.05/8.74 [0 0 0] [1] [0 0 0] [1] 32.05/8.74 32.05/8.74 [1 0 1] [1] [1 0 0] [0] 32.05/8.74 a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(a(b(x1))))) 32.05/8.74 [0 0 0] [1] [0 0 0] [1] 32.05/8.74 32.05/8.74 [1 1 1] [0] [1 0 1] [0] 32.05/8.74 a(b(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(b(a(x1))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [0] 32.05/8.75 32.05/8.75 [1 0 1] [0] [1 0 0] [0] 32.05/8.75 a(b(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(b(b(x1))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [0] 32.05/8.75 32.05/8.75 [1 1 1] [3] [1 1 1] [3] 32.05/8.75 a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(a(a(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [1] 32.05/8.75 32.05/8.75 [1 0 1] [2] [1 0 0] [2] 32.05/8.75 a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(a(b(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [1] 32.05/8.75 32.05/8.75 [1 1 1] [1] [1 0 1] [0] 32.05/8.75 a(a(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(b(a(b(a(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [1] 32.05/8.75 32.05/8.75 [1 0 1] [1] [1 0 0] [0] 32.05/8.75 a(a(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(b(a(b(b(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [1] 32.05/8.75 32.05/8.75 [1 1 1] [1] [1 1 1] [1] 32.05/8.75 a(b(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(b(a(a(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [0] 32.05/8.75 32.05/8.75 [1 0 1] [0] [1 0 0] [0] 32.05/8.75 a(b(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(b(b(a(b(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [0] 32.05/8.75 32.05/8.75 [1 1 1] [0] [1 0 1] [0] 32.05/8.75 a(b(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(a(b(b(b(a(x1))))))) 32.05/8.75 [0 0 0] [1] [0 0 0] [0] 32.05/8.76 32.05/8.76 [1 0 1] [0] [1 0 0] [0] 32.05/8.76 a(b(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(b(b(b(b(b(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] [0] 32.05/8.76 problem: 32.05/8.76 a(a(x1)) -> b(x1) 32.05/8.76 a(b(a(x1))) -> b(b(b(x1))) 32.05/8.76 a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) 32.05/8.76 a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) 32.05/8.76 a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) 32.05/8.76 a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) 32.05/8.76 a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) 32.05/8.76 a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) 32.05/8.76 a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) 32.05/8.76 a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) 32.05/8.76 Matrix Interpretation Processor: dim=3 32.05/8.76 32.05/8.76 interpretation: 32.05/8.76 [1 0 1] 32.05/8.76 [b](x0) = [0 0 0]x0 32.05/8.76 [0 0 0] , 32.05/8.76 32.05/8.76 [1 0 1] [0] 32.05/8.76 [a](x0) = [0 0 0]x0 + [1] 32.05/8.76 [0 1 0] [0] 32.05/8.76 orientation: 32.05/8.76 [1 1 1] [0] [1 0 1] 32.05/8.76 a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(x1) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [0] [1 0 1] 32.05/8.76 a(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(b(x1))) 32.05/8.76 [0 0 0] [0] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [1] [1 1 1] 32.05/8.76 a(b(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(b(b(a(x1))))) 32.05/8.76 [0 0 0] [0] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [0] [1 0 1] 32.05/8.76 a(b(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(b(b(b(x1))))) 32.05/8.76 [0 0 0] [0] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [3] [1 1 1] [3] 32.05/8.76 a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(a(a(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] [1] 32.05/8.76 32.05/8.76 [1 1 1] [1] [1 0 1] [1] 32.05/8.76 a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(a(b(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] [1] 32.05/8.76 32.05/8.76 [1 1 1] [2] [1 1 1] [2] 32.05/8.76 a(b(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(a(a(b(b(a(a(x1))))))) 32.05/8.76 [0 0 0] [0] [0 0 0] [0] 32.05/8.76 32.05/8.76 [1 1 1] [0] [1 0 1] 32.05/8.76 a(b(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(b(b(b(a(b(x1))))))) 32.05/8.76 [0 0 0] [0] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [1] [1 1 1] 32.05/8.76 a(b(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(a(b(b(b(a(x1))))))) 32.05/8.76 [0 0 0] [0] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [0] [1 0 1] 32.05/8.76 a(b(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(b(b(b(b(b(x1))))))) 32.05/8.76 [0 0 0] [0] [0 0 0] 32.05/8.76 problem: 32.05/8.76 a(a(x1)) -> b(x1) 32.05/8.76 a(b(a(x1))) -> b(b(b(x1))) 32.05/8.76 a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) 32.05/8.76 a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) 32.05/8.76 a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) 32.05/8.76 a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) 32.05/8.76 a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) 32.05/8.76 a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) 32.05/8.76 String Reversal Processor: 32.05/8.76 a(a(x1)) -> b(x1) 32.05/8.76 a(b(a(x1))) -> b(b(b(x1))) 32.05/8.76 a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) 32.05/8.76 a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) 32.05/8.76 a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) 32.05/8.76 a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) 32.05/8.76 a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) 32.05/8.76 a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) 32.05/8.76 Matrix Interpretation Processor: dim=3 32.05/8.76 32.05/8.76 interpretation: 32.05/8.76 [1 0 0] 32.05/8.76 [b](x0) = [0 0 0]x0 32.05/8.76 [0 0 0] , 32.05/8.76 32.05/8.76 [1 1 0] [0] 32.05/8.76 [a](x0) = [0 0 1]x0 + [0] 32.05/8.76 [0 0 0] [1] 32.05/8.76 orientation: 32.05/8.76 [1 1 1] [0] [1 0 0] 32.05/8.76 a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(x1) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 0] [0] [1 0 0] 32.05/8.76 a(b(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(x1))) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 0] [0] [1 0 0] 32.05/8.76 a(b(b(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(x1))))) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 1] [3] [1 1 1] [2] 32.05/8.76 a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(a(a(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] [1] 32.05/8.76 32.05/8.76 [1 1 1] [1] [1 1 1] 32.05/8.76 a(b(a(a(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(a(b(b(a(a(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 0] [1] [1 0 0] [0] 32.05/8.76 a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(a(b(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] [1] 32.05/8.76 32.05/8.76 [1 1 0] [0] [1 0 0] 32.05/8.76 a(b(a(b(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(b(b(b(a(b(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 32.05/8.76 [1 1 0] [0] [1 0 0] 32.05/8.76 a(b(b(b(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(b(b(x1))))))) 32.05/8.76 [0 0 0] [1] [0 0 0] 32.05/8.76 problem: 32.05/8.76 a(a(x1)) -> b(x1) 32.05/8.76 a(b(a(x1))) -> b(b(b(x1))) 32.05/8.76 a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) 32.05/8.76 a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) 32.05/8.76 a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) 32.05/8.76 KBO Processor: 32.05/8.76 weight function: 32.05/8.76 w0 = 1 32.05/8.76 w(a) = 1 32.05/8.76 w(b) = 0 32.05/8.76 precedence: 32.05/8.76 b > a 32.05/8.76 problem: 32.05/8.76 32.05/8.76 Qed 32.05/8.77 EOF