YES(?,O(n^1)) 0.16/0.25 YES(?,O(n^1)) 0.16/0.25 0.16/0.25 Problem: 0.16/0.25 f(s(X),X) -> f(X,a(X)) 0.16/0.25 f(X,c(X)) -> f(s(X),X) 0.16/0.25 f(X,X) -> c(X) 0.16/0.25 0.16/0.25 Proof: 0.16/0.25 Complexity Transformation Processor: 0.16/0.25 strict: 0.16/0.25 f(s(X),X) -> f(X,a(X)) 0.16/0.25 f(X,c(X)) -> f(s(X),X) 0.16/0.25 f(X,X) -> c(X) 0.16/0.25 weak: 0.16/0.25 0.16/0.25 Matrix Interpretation Processor: dim=1 0.16/0.25 0.16/0.25 max_matrix: 0.16/0.25 1 0.16/0.25 interpretation: 0.16/0.25 [c](x0) = x0, 0.16/0.25 0.16/0.25 [a](x0) = x0 + 19, 0.16/0.25 0.16/0.25 [f](x0, x1) = x0 + x1 + 237, 0.16/0.25 0.16/0.25 [s](x0) = x0 + 64 0.16/0.25 orientation: 0.16/0.25 f(s(X),X) = 2X + 301 >= 2X + 256 = f(X,a(X)) 0.16/0.25 0.16/0.25 f(X,c(X)) = 2X + 237 >= 2X + 301 = f(s(X),X) 0.16/0.25 0.16/0.25 f(X,X) = 2X + 237 >= X = c(X) 0.16/0.25 problem: 0.16/0.25 strict: 0.16/0.25 f(X,c(X)) -> f(s(X),X) 0.16/0.25 weak: 0.16/0.25 f(s(X),X) -> f(X,a(X)) 0.16/0.25 f(X,X) -> c(X) 0.16/0.25 Matrix Interpretation Processor: dim=1 0.16/0.25 0.16/0.25 max_matrix: 0.16/0.25 1 0.16/0.25 interpretation: 0.16/0.25 [c](x0) = x0 + 178, 0.16/0.25 0.16/0.25 [a](x0) = x0 + 6, 0.16/0.25 0.16/0.25 [f](x0, x1) = x0 + x1 + 178, 0.16/0.25 0.16/0.25 [s](x0) = x0 + 6 0.16/0.25 orientation: 0.16/0.25 f(X,c(X)) = 2X + 356 >= 2X + 184 = f(s(X),X) 0.16/0.25 0.16/0.25 f(s(X),X) = 2X + 184 >= 2X + 184 = f(X,a(X)) 0.16/0.25 0.16/0.25 f(X,X) = 2X + 178 >= X + 178 = c(X) 0.16/0.27 problem: 0.16/0.27 strict: 0.16/0.27 0.16/0.27 weak: 0.16/0.27 f(X,c(X)) -> f(s(X),X) 0.16/0.27 f(s(X),X) -> f(X,a(X)) 0.16/0.27 f(X,X) -> c(X) 0.16/0.27 Qed 0.16/0.27 EOF