YES(?,O(n^1)) TRS: { filter(cons X, 0(), M) -> cons 0(), filter(cons X, s N, M) -> cons X, sieve cons 0() -> cons 0(), sieve cons s N -> cons s N, nats N -> cons N, zprimes() -> sieve nats s s 0() } DUP: We consider a non-duplicating system. Trs: { filter(cons X, 0(), M) -> cons 0(), filter(cons X, s N, M) -> cons X, sieve cons 0() -> cons 0(), sieve cons s N -> cons s N, nats N -> cons N, zprimes() -> sieve nats s s 0() } Natural interpretation: Strict: { filter(cons X, 0(), M) -> cons 0(), filter(cons X, s N, M) -> cons X, sieve cons 0() -> cons 0(), sieve cons s N -> cons s N, nats N -> cons N, zprimes() -> sieve nats s s 0() } Weak: {} Interpretation class: stronglylinear [zprimes] = + 7 [nats](X0) = + 1*X0 + 5 [sieve](X0) = + 1*X0 + 1 [s](X0) = + 1*X0 + 0 [filter](X2, X1, X0) = + 1*X0 + 1*X1 + 1*X2 + 4 [0] = + 0 [cons](X0) = + 1*X0 + 0 Qed