13.84/3.81 YES 13.84/3.82 13.84/3.82 Problem: 13.84/3.82 b(b(x1)) -> b(a(b(a(a(b(x1)))))) 13.84/3.82 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 13.84/3.82 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(a(b(b(x1)))))) 13.84/3.82 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1))))) 13.84/3.82 13.84/3.82 Proof: 13.84/3.82 Matrix Interpretation Processor: dim=4 13.84/3.82 13.84/3.82 interpretation: 13.84/3.82 [1 0 0 1] [0] 13.84/3.82 [0 0 1 0] [1] 13.84/3.82 [a](x0) = [0 0 0 0]x0 + [0] 13.84/3.82 [0 1 0 0] [0], 13.84/3.82 13.84/3.82 [1 0 0 0] 13.84/3.82 [0 0 0 0] 13.84/3.82 [b](x0) = [0 0 1 1]x0 13.84/3.82 [0 0 0 0] 13.84/3.82 orientation: 13.84/3.82 [1 0 0 0] [1 0 0 0] 13.84/3.82 [0 0 0 0] [0 0 0 0] 13.84/3.82 b(b(x1)) = [0 0 1 1]x1 >= [0 0 0 0]x1 = b(a(b(a(a(b(x1)))))) 13.84/3.82 [0 0 0 0] [0 0 0 0] 13.84/3.82 13.84/3.82 [1 0 0 0] [1 0 0 0] 13.84/3.82 [0 0 0 0] [0 0 0 0] 13.84/3.82 b(b(a(b(x1)))) = [0 0 0 0]x1 >= [0 0 0 0]x1 = b(a(b(b(x1)))) 13.84/3.82 [0 0 0 0] [0 0 0 0] 13.84/3.82 13.84/3.82 [1 0 1 1] [2] [1 0 1 1] [1] 13.84/3.82 [0 0 0 0] [0] [0 0 0 0] [0] 13.84/3.82 b(a(a(a(b(a(a(b(x1)))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(a(a(b(b(x1)))))) 13.84/3.82 [0 0 0 0] [0] [0 0 0 0] [0] 13.84/3.82 13.84/3.82 [1 0 0 0] [0] [1 0 0 0] [0] 13.84/3.82 [0 0 0 0] [0] [0 0 0 0] [0] 13.84/3.82 b(b(a(a(b(x1))))) = [0 0 1 1]x1 + [1] >= [0 0 1 1]x1 + [1] = b(a(a(b(b(x1))))) 13.84/3.82 [0 0 0 0] [0] [0 0 0 0] [0] 13.84/3.82 problem: 13.84/3.82 b(b(x1)) -> b(a(b(a(a(b(x1)))))) 13.84/3.82 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 13.84/3.82 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1))))) 13.84/3.82 Matrix Interpretation Processor: dim=3 13.84/3.82 13.84/3.82 interpretation: 13.84/3.82 [1 0 0] 13.84/3.82 [a](x0) = [0 0 0]x0 13.84/3.82 [0 0 0] , 13.84/3.82 13.84/3.82 [1 0 1] [0] 13.84/3.82 [b](x0) = [0 0 0]x0 + [0] 13.84/3.82 [0 0 0] [1] 13.84/3.82 orientation: 13.84/3.82 [1 0 1] [1] [1 0 1] [0] 13.84/3.82 b(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(b(a(a(b(x1)))))) 13.84/3.82 [0 0 0] [1] [0 0 0] [1] 13.84/3.82 13.84/3.82 [1 0 1] [1] [1 0 1] [1] 13.84/3.82 b(b(a(b(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(b(b(x1)))) 13.84/3.82 [0 0 0] [1] [0 0 0] [1] 13.84/3.82 13.84/3.82 [1 0 1] [1] [1 0 1] [1] 13.84/3.82 b(b(a(a(b(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(a(b(b(x1))))) 13.84/3.82 [0 0 0] [1] [0 0 0] [1] 13.84/3.82 problem: 13.84/3.82 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 13.84/3.82 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1))))) 13.84/3.82 KBO Processor: 13.84/3.82 weight function: 13.84/3.82 w0 = 1 13.84/3.82 w(a) = 1 13.84/3.82 w(b) = 0 13.84/3.82 precedence: 13.84/3.82 b > a 13.84/3.82 problem: 13.84/3.82 13.84/3.82 Qed 13.84/3.83 EOF