TRS: { not(true()) -> false(), not(false()) -> true(), odd(0()) -> false(), odd(s(x)) -> not(odd(x)), +(x, 0()) -> x, +(x, s(y)) -> s(+(x, y)), +(s(x), y) -> s(+(x, y))} RPO Product: Quasi-Precedence: odd > not empty Qed TRS: { not(true()) -> false(), not(false()) -> true(), odd(0()) -> false(), odd(s(x)) -> not(odd(x)), +(x, 0()) -> x, +(x, s(y)) -> s(+(x, y)), +(s(x), y) -> s(+(x, y))} Cdiprover: Interpretation class: quasisimplemixed Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING +(X4, X3) = + 0*X4^2 + 0*X3^2 + 1*X4 + 0 + 1*X3 + 0*X3*X4 s(X2) = + 1*X2 + 1 0 = + 0 odd(X1) = + 0*X1^2 + 0 + 1*X1 true = + 0 not(X0) = + 0*X0^2 + 1 + 1*X0 false = + 0 Qed