TRS: { terms(N) -> cons(recip(sqr(N))), sqr(0()) -> 0(), sqr(s(X)) -> s(add(sqr(X), dbl(X))), dbl(0()) -> 0(), dbl(s(X)) -> s(s(dbl(X))), add(0(), X) -> X, add(s(X), Y) -> s(add(X, Y)), first(0(), X) -> nil(), first(s(X), cons(Y)) -> cons(Y)} RPO Product: Quasi-Precedence: terms > sqr ~ dbl, sqr ~ dbl > add empty Qed TRS: { terms(N) -> cons(recip(sqr(N))), sqr(0()) -> 0(), sqr(s(X)) -> s(add(sqr(X), dbl(X))), dbl(0()) -> 0(), dbl(s(X)) -> s(s(dbl(X))), add(0(), X) -> X, add(s(X), Y) -> s(add(X, Y)), first(0(), X) -> nil(), first(s(X), cons(Y)) -> cons(Y)} Cdiprover: Interpretation class: quasisimplemixed Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING first(X9, X8) = + 0*X9^2 + 0*X8^2 + 2*X9 + 2 + 1*X8 + 0*X8*X9 nil = + 0 dbl(X7) = + 0*X7^2 + 2 + 2*X7 add(X6, X5) = + 0*X6^2 + 0*X5^2 + 1*X6 + 0 + 1*X5 + 0*X5*X6 s(X4) = + 1*X4 + 3 0 = + 0 terms(X3) = + 1*X3^2 + 3 + 1*X3 sqr(X2) = + 1*X2^2 + 0 + 1*X2 recip(X1) = + 1*X1 + 1 cons(X0) = + 1*X0 + 2 Qed