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