43.42/11.38 YES 43.42/11.39 43.42/11.39 Problem: 43.42/11.39 p(0(x1)) -> s(s(0(s(s(p(x1)))))) 43.42/11.39 p(s(0(x1))) -> 0(x1) 43.42/11.39 p(s(s(x1))) -> s(p(s(x1))) 43.42/11.39 f(s(x1)) -> g(q(i(x1))) 43.42/11.39 g(x1) -> f(p(p(x1))) 43.42/11.39 q(i(x1)) -> q(s(x1)) 43.42/11.39 q(s(x1)) -> s(s(x1)) 43.42/11.39 i(x1) -> s(x1) 43.42/11.39 43.42/11.39 Proof: 43.42/11.39 Matrix Interpretation Processor: dim=4 43.42/11.39 43.42/11.39 interpretation: 43.42/11.39 [1 1 0 1] [0] 43.42/11.39 [0 1 0 0] [0] 43.42/11.39 [g](x0) = [0 0 0 0]x0 + [1] 43.42/11.39 [0 0 0 0] [0], 43.42/11.39 43.42/11.39 [1 0 0 0] 43.42/11.39 [0 0 0 0] 43.42/11.39 [q](x0) = [0 0 1 1]x0 43.42/11.39 [0 0 0 0] , 43.42/11.39 43.42/11.39 [1 0 0 0] [0] 43.42/11.39 [0 0 1 0] [1] 43.42/11.39 [i](x0) = [0 0 1 1]x0 + [1] 43.42/11.39 [0 1 1 0] [1], 43.42/11.39 43.42/11.39 [1 0 0 0] [0] 43.42/11.39 [0 0 0 0] [0] 43.42/11.39 [f](x0) = [0 0 0 0]x0 + [1] 43.42/11.39 [0 0 0 0] [0], 43.42/11.39 43.42/11.39 [1 0 0 0] 43.42/11.39 [0 0 1 0] 43.42/11.39 [s](x0) = [0 0 0 0]x0 43.42/11.39 [0 0 0 0] , 43.42/11.39 43.42/11.39 [1 0 0 1] 43.42/11.39 [1 0 0 0] 43.42/11.39 [p](x0) = [1 0 0 0]x0 43.42/11.39 [0 1 0 0] , 43.42/11.39 43.42/11.39 [1 0 0 1] [1] 43.42/11.39 [0 0 0 0] [0] 43.42/11.40 [0](x0) = [0 0 0 0]x0 + [1] 43.42/11.40 [0 0 0 0] [1] 43.42/11.40 orientation: 43.42/11.40 [1 0 0 1] [2] [1 0 0 1] [1] 43.42/11.40 [1 0 0 1] [1] [0 0 0 0] [0] 43.42/11.40 p(0(x1)) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [0] = s(s(0(s(s(p(x1)))))) 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] [0] 43.42/11.40 43.42/11.40 [1 0 0 1] [1] [1 0 0 1] [1] 43.42/11.40 [1 0 0 1] [1] [0 0 0 0] [0] 43.42/11.40 p(s(0(x1))) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = 0(x1) 43.42/11.40 [0 0 0 0] [1] [0 0 0 0] [1] 43.42/11.40 43.42/11.40 [1 0 0 0] [1 0 0 0] 43.42/11.40 [1 0 0 0] [1 0 0 0] 43.42/11.40 p(s(s(x1))) = [1 0 0 0]x1 >= [0 0 0 0]x1 = s(p(s(x1))) 43.42/11.40 [0 0 0 0] [0 0 0 0] 43.42/11.40 43.42/11.40 [1 0 0 0] [0] [1 0 0 0] [0] 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] [0] 43.42/11.40 f(s(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = g(q(i(x1))) 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] [0] 43.42/11.40 43.42/11.40 [1 1 0 1] [0] [1 1 0 1] [0] 43.42/11.40 [0 1 0 0] [0] [0 0 0 0] [0] 43.42/11.40 g(x1) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = f(p(p(x1))) 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] [0] 43.42/11.40 43.42/11.40 [1 0 0 0] [0] [1 0 0 0] 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] 43.42/11.40 q(i(x1)) = [0 1 2 1]x1 + [2] >= [0 0 0 0]x1 = q(s(x1)) 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] 43.42/11.40 43.42/11.40 [1 0 0 0] [1 0 0 0] 43.42/11.40 [0 0 0 0] [0 0 0 0] 43.42/11.40 q(s(x1)) = [0 0 0 0]x1 >= [0 0 0 0]x1 = s(s(x1)) 43.42/11.40 [0 0 0 0] [0 0 0 0] 43.42/11.40 43.42/11.40 [1 0 0 0] [0] [1 0 0 0] 43.42/11.40 [0 0 1 0] [1] [0 0 1 0] 43.42/11.40 i(x1) = [0 0 1 1]x1 + [1] >= [0 0 0 0]x1 = s(x1) 43.42/11.40 [0 1 1 0] [1] [0 0 0 0] 43.42/11.40 problem: 43.42/11.40 p(s(0(x1))) -> 0(x1) 43.42/11.40 p(s(s(x1))) -> s(p(s(x1))) 43.42/11.40 f(s(x1)) -> g(q(i(x1))) 43.42/11.40 g(x1) -> f(p(p(x1))) 43.42/11.40 q(i(x1)) -> q(s(x1)) 43.42/11.40 q(s(x1)) -> s(s(x1)) 43.42/11.40 i(x1) -> s(x1) 43.42/11.40 Matrix Interpretation Processor: dim=4 43.42/11.40 43.42/11.40 interpretation: 43.42/11.40 [1 0 1 0] 43.42/11.40 [0 0 0 0] 43.42/11.40 [g](x0) = [0 0 0 0]x0 43.42/11.40 [0 0 0 0] , 43.42/11.40 43.42/11.40 [1 0 0 0] [0] 43.42/11.40 [1 1 1 1] [1] 43.42/11.40 [q](x0) = [0 0 0 1]x0 + [0] 43.42/11.40 [1 1 0 0] [0], 43.42/11.40 43.42/11.40 [1 0 0 1] [0] 43.42/11.40 [1 1 0 1] [1] 43.42/11.40 [i](x0) = [1 1 1 1]x0 + [0] 43.42/11.40 [0 1 0 0] [0], 43.42/11.40 43.42/11.40 [1 1 0 0] 43.42/11.40 [0 0 0 0] 43.42/11.40 [f](x0) = [0 0 0 0]x0 43.42/11.40 [0 0 0 0] , 43.42/11.40 43.42/11.40 [1 0 0 0] [0] 43.42/11.40 [0 1 0 1] [1] 43.42/11.40 [s](x0) = [0 0 0 1]x0 + [0] 43.42/11.40 [0 1 0 0] [0], 43.42/11.40 43.42/11.40 [1 0 0 0] 43.42/11.40 [0 0 0 1] 43.42/11.40 [p](x0) = [0 1 0 0]x0 43.42/11.40 [0 0 1 0] , 43.42/11.40 43.42/11.40 [1 0 0 0] 43.42/11.40 [0 0 1 1] 43.42/11.40 [0](x0) = [0 0 0 0]x0 43.42/11.40 [0 0 0 0] 43.42/11.40 orientation: 43.42/11.40 [1 0 0 0] [0] [1 0 0 0] 43.42/11.40 [0 0 1 1] [0] [0 0 1 1] 43.42/11.40 p(s(0(x1))) = [0 0 1 1]x1 + [1] >= [0 0 0 0]x1 = 0(x1) 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] 43.42/11.40 43.42/11.40 [1 0 0 0] [0] [1 0 0 0] [0] 43.42/11.40 [0 1 0 1] [1] [0 1 0 1] [1] 43.42/11.40 p(s(s(x1))) = [0 2 0 1]x1 + [2] >= [0 0 0 1]x1 + [0] = s(p(s(x1))) 43.42/11.40 [0 1 0 0] [0] [0 1 0 0] [0] 43.42/11.40 43.42/11.40 [1 1 0 1] [1] [1 1 0 1] 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] 43.42/11.40 f(s(x1)) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 = g(q(i(x1))) 43.42/11.40 [0 0 0 0] [0] [0 0 0 0] 43.42/11.40 43.42/11.40 [1 0 1 0] [1 0 1 0] 43.42/11.40 [0 0 0 0] [0 0 0 0] 43.42/11.40 g(x1) = [0 0 0 0]x1 >= [0 0 0 0]x1 = f(p(p(x1))) 43.42/11.40 [0 0 0 0] [0 0 0 0] 43.42/11.40 43.42/11.40 [1 0 0 1] [0] [1 0 0 0] [0] 43.42/11.40 [3 3 1 3] [2] [1 2 0 2] [2] 43.42/11.40 q(i(x1)) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = q(s(x1)) 43.42/11.40 [2 1 0 2] [1] [1 1 0 1] [1] 43.42/11.40 43.42/11.40 [1 0 0 0] [0] [1 0 0 0] [0] 43.42/11.40 [1 2 0 2] [2] [0 2 0 1] [2] 43.42/11.40 q(s(x1)) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = s(s(x1)) 43.42/11.40 [1 1 0 1] [1] [0 1 0 1] [1] 43.42/11.40 43.42/11.40 [1 0 0 1] [0] [1 0 0 0] [0] 43.42/11.40 [1 1 0 1] [1] [0 1 0 1] [1] 43.42/11.40 i(x1) = [1 1 1 1]x1 + [0] >= [0 0 0 1]x1 + [0] = s(x1) 43.42/11.40 [0 1 0 0] [0] [0 1 0 0] [0] 43.42/11.40 problem: 43.42/11.40 p(s(0(x1))) -> 0(x1) 43.42/11.40 p(s(s(x1))) -> s(p(s(x1))) 43.42/11.40 g(x1) -> f(p(p(x1))) 43.42/11.40 q(i(x1)) -> q(s(x1)) 43.42/11.40 q(s(x1)) -> s(s(x1)) 43.42/11.40 i(x1) -> s(x1) 43.42/11.40 KBO Processor: 43.42/11.40 weight function: 43.42/11.40 w0 = 1 43.42/11.40 w(g) = w(q) = w(i) = w(f) = w(s) = w(0) = 1 43.42/11.40 w(p) = 0 43.42/11.40 precedence: 43.42/11.40 p > g ~ q ~ i > f ~ s ~ 0 43.42/11.40 problem: 43.42/11.40 43.42/11.40 Qed 43.42/11.41 EOF