MAYBE
MAYBE
TRS:
 {
                   cons(mark(X1), X2) -> mark(cons(X1, X2)),
                 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
             filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3)),
             filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3)),
             filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3)),
       filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3)),
                 active(cons(X1, X2)) -> cons(active(X1), X2),
           active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)),
           active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3),
           active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3),
   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(s(X)) -> s(active(X)),
                     active(sieve(X)) -> sieve(active(X)),
          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(X)) -> nats(active(X)),
                      active(nats(N)) -> mark(cons(N, nats(s(N)))),
                    active(zprimes()) -> mark(sieve(nats(s(s(0()))))),
                           s(mark(X)) -> mark(s(X)),
                             s(ok(X)) -> ok(s(X)),
                       sieve(mark(X)) -> mark(sieve(X)),
                         sieve(ok(X)) -> ok(sieve(X)),
                        nats(mark(X)) -> mark(nats(X)),
                          nats(ok(X)) -> ok(nats(X)),
                 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                          proper(0()) -> ok(0()),
           proper(filter(X1, X2, X3)) ->
  filter(proper(X1), proper(X2), proper(X3)),
                         proper(s(X)) -> s(proper(X)),
                     proper(sieve(X)) -> sieve(proper(X)),
                      proper(nats(X)) -> nats(proper(X)),
                    proper(zprimes()) -> ok(zprimes()),
                         top(mark(X)) -> top(proper(X)),
                           top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                     cons(mark(X1), X2) -> mark(cons(X1, X2)),
                   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
               filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3)),
               filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3)),
               filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3)),
         filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3)),
                   active(cons(X1, X2)) -> cons(active(X1), X2),
             active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)),
             active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3),
             active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3),
     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(s(X)) -> s(active(X)),
                       active(sieve(X)) -> sieve(active(X)),
            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(X)) -> nats(active(X)),
                        active(nats(N)) -> mark(cons(N, nats(s(N)))),
                      active(zprimes()) -> mark(sieve(nats(s(s(0()))))),
                             s(mark(X)) -> mark(s(X)),
                               s(ok(X)) -> ok(s(X)),
                         sieve(mark(X)) -> mark(sieve(X)),
                           sieve(ok(X)) -> ok(sieve(X)),
                          nats(mark(X)) -> mark(nats(X)),
                            nats(ok(X)) -> ok(nats(X)),
                   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                            proper(0()) -> ok(0()),
             proper(filter(X1, X2, X3)) ->
    filter(proper(X1), proper(X2), proper(X3)),
                           proper(s(X)) -> s(proper(X)),
                       proper(sieve(X)) -> sieve(proper(X)),
                        proper(nats(X)) -> nats(proper(X)),
                      proper(zprimes()) -> ok(zprimes()),
                           top(mark(X)) -> top(proper(X)),
                             top(ok(X)) -> top(active(X))
   }
  Fail