TRS: { sum(0()) -> 0(), sum(s(x)) -> +(sum(x), s(x)), sum1(0()) -> 0(), sum1(s(x)) -> s(+(sum1(x), +(x, x)))} RPO Product: Quasi-Precedence: empty Qed TRS: { sum(0()) -> 0(), sum(s(x)) -> +(sum(x), s(x)), sum1(0()) -> 0(), sum1(s(x)) -> s(+(sum1(x), +(x, x)))} Cdiprover: Interpretation class: quasisimplemixed Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING sum1(X4) = + 2*X4^2 + 2 + 3*X4 s(X3) = + 1*X3 + 3 +(X2, X1) = + 1*X1 + 1*X2 + 1 sum(X0) = + 2*X0^2 + 2 + 1*X0 0 = + 0 Qed