TRS: { terms(N) -> cons(recip(sqr(N))), sqr(0()) -> 0(), sqr(s()) -> s(), dbl(0()) -> 0(), dbl(s()) -> s(), add(0(), X) -> X, add(s(), Y) -> s(), first(0(), X) -> nil(), first(s(), cons(Y)) -> cons(Y)} RPO Product: Quasi-Precedence: terms > sqr empty Qed TRS: { terms(N) -> cons(recip(sqr(N))), sqr(0()) -> 0(), sqr(s()) -> s(), dbl(0()) -> 0(), dbl(s()) -> s(), add(0(), X) -> X, add(s(), Y) -> s(), first(0(), X) -> nil(), first(s(), cons(Y)) -> cons(Y)} Cdiprover: Interpretation class: quasisimplemixed Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING first(X8, X7) = + 0*X8^2 + 0*X7^2 + 2*X8 + 1 + 2*X7 + 0*X7*X8 nil = + 0 add(X6, X5) = + 0*X6^2 + 2*X5^2 + 1*X6 + 2 + 2*X5 + 0*X5*X6 dbl(X4) = + 0*X4^2 + 2 + 1*X4 s = + 0 0 = + 0 terms(X3) = + 0*X3^2 + 3 + 3*X3 sqr(X2) = + 0*X2^2 + 0 + 2*X2 recip(X1) = + 1*X1 + 1 cons(X0) = + 1*X0 + 1 Qed