MAYBE
MAYBE
TRS:
 {
                      activate(X) -> X,
  activate(n__filter(X1, X2, X3)) ->
  filter(activate(X1), activate(X2), activate(X3)),
            activate(n__sieve(X)) -> sieve(activate(X)),
             activate(n__nats(X)) -> nats(activate(X)),
                activate(n__s(X)) -> s(activate(X)),
               filter(X1, X2, X3) -> n__filter(X1, X2, X3),
       filter(cons(X, Y), 0(), M) -> cons(0(), n__filter(activate(Y), M, M)),
      filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)),
                             s(X) -> n__s(X),
                         sieve(X) -> n__sieve(X),
              sieve(cons(0(), Y)) -> cons(0(), n__sieve(activate(Y))),
             sieve(cons(s(N), Y)) ->
  cons(s(N), n__sieve(n__filter(activate(Y), N, N))),
                          nats(X) -> n__nats(X),
                          nats(N) -> cons(N, n__nats(n__s(N))),
                        zprimes() -> sieve(nats(s(s(0()))))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                        activate(X) -> X,
    activate(n__filter(X1, X2, X3)) ->
    filter(activate(X1), activate(X2), activate(X3)),
              activate(n__sieve(X)) -> sieve(activate(X)),
               activate(n__nats(X)) -> nats(activate(X)),
                  activate(n__s(X)) -> s(activate(X)),
                 filter(X1, X2, X3) -> n__filter(X1, X2, X3),
         filter(cons(X, Y), 0(), M) ->
    cons(0(), n__filter(activate(Y), M, M)),
        filter(cons(X, Y), s(N), M) -> cons(X, n__filter(activate(Y), N, M)),
                               s(X) -> n__s(X),
                           sieve(X) -> n__sieve(X),
                sieve(cons(0(), Y)) -> cons(0(), n__sieve(activate(Y))),
               sieve(cons(s(N), Y)) ->
    cons(s(N), n__sieve(n__filter(activate(Y), N, N))),
                            nats(X) -> n__nats(X),
                            nats(N) -> cons(N, n__nats(n__s(N))),
                          zprimes() -> sieve(nats(s(s(0()))))
   }
  Fail