MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { filter(X1, X2, X3) -> n__filter(X1, X2, X3) , filter(cons(X, Y), 0(), M) -> cons(0(), n__filter(activate(Y), M, M)) , filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)) , activate(X) -> X , activate(n__filter(X1, X2, X3)) -> filter(X1, X2, X3) , activate(n__sieve(X)) -> sieve(X) , activate(n__nats(X)) -> nats(X) , sieve(X) -> n__sieve(X) , sieve(cons(0(), Y)) -> cons(0(), n__sieve(activate(Y))) , sieve(cons(s(N), Y)) -> cons(s(N), n__sieve(filter(activate(Y), N, N))) , nats(N) -> cons(N, n__nats(s(N))) , nats(X) -> n__nats(X) , zprimes() -> sieve(nats(s(s(0())))) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..