MAYBE
Trs:
 {           filter(mark(X1), X2, X3) -> filter(X1, X2, X3),
           filter(active(X1), X2, X3) -> filter(X1, X2, X3),
             filter(X1, mark(X2), X3) -> filter(X1, X2, X3),
           filter(X1, active(X2), X3) -> filter(X1, X2, X3),
             filter(X1, X2, mark(X3)) -> filter(X1, X2, X3),
           filter(X1, X2, active(X3)) -> filter(X1, X2, X3),
                   cons(mark(X1), X2) -> cons(X1, X2),
                 cons(active(X1), X2) -> cons(X1, X2),
                   cons(X1, mark(X2)) -> cons(X1, X2),
                 cons(X1, active(X2)) -> cons(X1, X2),
                           s(mark(X)) -> s(X),
                         s(active(X)) -> s(X),
                       sieve(mark(X)) -> sieve(X),
                     sieve(active(X)) -> sieve(X),
                            mark(0()) -> active(0()),
                      mark(zprimes()) -> active(zprimes()),
             mark(filter(X1, X2, X3)) -> active(filter(mark(X1), mark(X2), mark(X3))),
                   mark(cons(X1, X2)) -> active(cons(mark(X1), X2)),
                           mark(s(X)) -> active(s(mark(X))),
                       mark(sieve(X)) -> active(sieve(mark(X))),
                        mark(nats(X)) -> active(nats(mark(X))),
                    active(zprimes()) -> mark(sieve(nats(s(s(0()))))),
   active(filter(cons(X, Y), 0(), M)) -> mark(cons(0(), filter(Y, M, M))),
  active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))),
          active(sieve(cons(0(), Y))) -> mark(cons(0(), sieve(Y))),
         active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))),
                      active(nats(N)) -> mark(cons(N, nats(s(N)))),
                        nats(mark(X)) -> nats(X),
                      nats(active(X)) -> nats(X)}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open