YES Trs: { filter(cons(X), 0(), M) -> cons(0()), filter(cons(X), s(N), M) -> cons(X), zprimes() -> sieve(nats(s(s(0())))), nats(N) -> cons(N), sieve(cons(0())) -> cons(0()), sieve(cons(s(N))) -> cons(s(N))} Comment: We consider a non-duplicating trs. BOUND: Automaton: {filter_0(q7, q7, q7) -> q7, cons_2(q9) -> q7, cons_2(q7) -> q8, cons_1(q9) -> q7, cons_1(q7) -> q7, cons_0(q7) -> q7, zprimes_0() -> q7, 0_2() -> q9, 0_1() -> q7, 0_0() -> q7, s_2(q7) -> q9, s_1(q7) -> q7, s_0(q7) -> q7, nats_1(q7) -> q8, nats_0(q7) -> q7, sieve_1(q8) -> q7, sieve_0(q7) -> q7} Strict: {} Qed