13.92/4.00 YES 13.92/4.00 13.92/4.00 Problem: 13.92/4.00 a(b(b(a(x1)))) -> b(a(a(b(x1)))) 13.92/4.00 b(a(b(x1))) -> a(b(b(b(x1)))) 13.92/4.00 13.92/4.00 Proof: 13.92/4.00 Matrix Interpretation Processor: dim=4 13.92/4.00 13.92/4.00 interpretation: 13.92/4.00 [1 0 0 0] 13.92/4.00 [1 0 0 0] 13.92/4.00 [b](x0) = [0 1 0 0]x0 13.92/4.00 [0 1 0 0] , 13.92/4.00 13.92/4.00 [1 1 0 0] [1] 13.92/4.00 [0 0 1 1] [0] 13.92/4.00 [a](x0) = [0 0 0 0]x0 + [0] 13.92/4.00 [0 0 0 0] [0] 13.92/4.00 orientation: 13.92/4.00 [2 2 0 0] [3] [2 2 0 0] [2] 13.92/4.00 [2 2 0 0] [2] [2 2 0 0] [2] 13.92/4.00 a(b(b(a(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(a(a(b(x1)))) 13.92/4.00 [0 0 0 0] [0] [0 0 0 0] [0] 13.92/4.00 13.92/4.00 [2 0 0 0] [1] [2 0 0 0] [1] 13.92/4.00 [2 0 0 0] [1] [2 0 0 0] [0] 13.92/4.00 b(a(b(x1))) = [0 2 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(b(b(b(x1)))) 13.92/4.00 [0 2 0 0] [0] [0 0 0 0] [0] 13.92/4.00 problem: 13.92/4.00 b(a(b(x1))) -> a(b(b(b(x1)))) 13.92/4.00 KBO Processor: 13.92/4.00 weight function: 13.92/4.00 w0 = 1 13.92/4.00 w(a) = 1 13.92/4.00 w(b) = 0 13.92/4.00 precedence: 13.92/4.00 b > a 13.92/4.00 problem: 13.92/4.00 13.92/4.00 Qed 13.92/4.01 EOF