YES O(n^5) 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())))) } Matrix Interpretation: Interpretation class: triangular [3] [3] [zprimes] = [2] [2] [2] [X4] [1 0 0 1 2][X4] [1] [X3] [0 0 0 0 2][X3] [3] [nats]([X2]) = [0 0 1 2 0][X2] + [0] [X1] [0 0 0 0 0][X1] [2] [X0] [0 0 0 0 0][X0] [0] [X4] [1 0 0 0 0][X4] [1] [X3] [0 0 0 1 0][X3] [1] [sieve]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [2] [X0] [0 0 0 0 0][X0] [0] [X4] [1 0 0 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [0] [s]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 0][X0] [0] [X14] [X9] [X4] [1 3 0 2 0][X14] [1 0 0 0 0][X9] [1 0 2 2 2][X4] [3] [X13] [X8] [X3] [0 1 0 0 0][X13] [0 0 0 0 0][X8] [0 0 2 0 2][X3] [2] [filter]([X12], [X7], [X2]) = [0 0 0 0 0][X12] + [0 0 0 0 0][X7] + [0 0 0 2 2][X2] + [0] [X11] [X6] [X1] [0 0 0 1 0][X11] [0 0 0 0 0][X6] [0 0 0 0 0][X1] [2] [X10] [X5] [X0] [0 0 0 0 0][X10] [0 0 0 0 0][X5] [0 0 0 0 0][X0] [0] [0] [0] [0] = [0] [0] [0] [X4] [1 0 0 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [3] [cons]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [2] [X0] [0 0 0 0 0][X0] [0] Qed