(VAR M N X X1 X2 X3 Y )
(RULES 
        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))))
        active(zprimes) -> mark(sieve(nats(s(s(0)))))
        active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3)
        active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3)
        active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3))
        active(cons(X1, X2)) -> cons(active(X1), X2)
        active(s(X)) -> s(active(X))
        active(sieve(X)) -> sieve(active(X))
        active(nats(X)) -> nats(active(X))
        filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3))
        filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3))
        filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        s(mark(X)) -> mark(s(X))
        sieve(mark(X)) -> mark(sieve(X))
        nats(mark(X)) -> mark(nats(X))
        proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3))
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(0) -> ok(0)
        proper(s(X)) -> s(proper(X))
        proper(sieve(X)) -> sieve(proper(X))
        proper(nats(X)) -> nats(proper(X))
        proper(zprimes) -> ok(zprimes)
        filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        s(ok(X)) -> ok(s(X))
        sieve(ok(X)) -> ok(sieve(X))
        nats(ok(X)) -> ok(nats(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)