TRS: { f(0()) -> s(0()), f(s(0())) -> s(s(0())), f(s(0())) -> *(s(s(0())), f(0())), f(+(x, s(0()))) -> +(s(s(0())), f(x)), f(+(x, y)) -> *(f(x), f(y))} RPO Product: Quasi-Precedence: empty Qed TRS: { f(0()) -> s(0()), f(s(0())) -> s(s(0())), f(s(0())) -> *(s(s(0())), f(0())), f(+(x, s(0()))) -> +(s(s(0())), f(x)), f(+(x, y)) -> *(f(x), f(y))} Cdiprover: Interpretation class: quasisimplemixed Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING +(X5, X4) = + 1*X4 + 1*X5 + 1 *(X3, X2) = + 1*X2 + 1*X3 + 1 f(X1) = + 2*X1^2 + 2 + 1*X1 0 = + 0 s(X0) = + 1*X0 + 1 Qed