YES(?,O(n^1)) 0.15/0.23 YES(?,O(n^1)) 0.15/0.23 0.15/0.23 Problem: 0.15/0.23 f(f(a())) -> f(g(n__f(a()))) 0.15/0.23 f(X) -> n__f(X) 0.15/0.23 activate(n__f(X)) -> f(X) 0.15/0.23 activate(X) -> X 0.15/0.23 0.15/0.23 Proof: 0.15/0.23 Complexity Transformation Processor: 0.15/0.23 strict: 0.15/0.23 f(f(a())) -> f(g(n__f(a()))) 0.15/0.23 f(X) -> n__f(X) 0.15/0.23 activate(n__f(X)) -> f(X) 0.15/0.23 activate(X) -> X 0.15/0.23 weak: 0.15/0.23 0.15/0.23 Matrix Interpretation Processor: dim=1 0.15/0.23 0.15/0.23 max_matrix: 0.15/0.23 1 0.15/0.23 interpretation: 0.15/0.23 [activate](x0) = x0 + 225, 0.15/0.23 0.15/0.23 [g](x0) = x0 + 10, 0.15/0.23 0.15/0.23 [n__f](x0) = x0 + 64, 0.15/0.23 0.15/0.23 [f](x0) = x0 + 106, 0.15/0.23 0.15/0.23 [a] = 204 0.15/0.23 orientation: 0.15/0.23 f(f(a())) = 416 >= 384 = f(g(n__f(a()))) 0.15/0.23 0.15/0.23 f(X) = X + 106 >= X + 64 = n__f(X) 0.15/0.23 0.15/0.23 activate(n__f(X)) = X + 289 >= X + 106 = f(X) 0.15/0.23 0.15/0.23 activate(X) = X + 225 >= X = X 0.15/0.23 problem: 0.15/0.23 strict: 0.15/0.23 0.15/0.23 weak: 0.15/0.23 f(f(a())) -> f(g(n__f(a()))) 0.15/0.23 f(X) -> n__f(X) 0.15/0.23 activate(n__f(X)) -> f(X) 0.15/0.23 activate(X) -> X 0.15/0.23 Qed 0.15/0.23 EOF