TRS: { f(X) -> g(n__h(n__f(X))), h(X) -> n__h(X), f(X) -> n__f(X), activate(n__h(X)) -> h(activate(X)), activate(n__f(X)) -> f(activate(X)), activate(X) -> X} RPO Product: Quasi-Precedence: activate > h, activate > f empty Qed TRS: { f(X) -> g(n__h(n__f(X))), h(X) -> n__h(X), f(X) -> n__f(X), activate(n__h(X)) -> h(activate(X)), activate(n__f(X)) -> f(activate(X)), activate(X) -> X} Cdiprover: Interpretation class: quasisimplemixed Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING activate(X5) = + 0*X5^2 + 0 + 3*X5 h(X4) = + 0*X4^2 + 2 + 1*X4 f(X3) = + 0*X3^2 + 3 + 1*X3 n__f(X2) = + 1*X2 + 1 n__h(X1) = + 1*X1 + 1 g(X0) = + 1*X0 + 1 Qed