MAYBE
MAYBE
TRS:
 {
                     sieve(X) -> n__sieve(X),
            sieve(cons(X, Y)) -> cons(X, n__filter(X, n__sieve(activate(Y)))),
                      from(X) -> cons(X, n__from(n__s(X))),
                      from(X) -> n__from(X),
                         s(X) -> n__s(X),
                     primes() -> sieve(from(s(s(0())))),
                 cons(X1, X2) -> n__cons(X1, X2),
             head(cons(X, Y)) -> X,
                  activate(X) -> X,
         activate(n__from(X)) -> from(activate(X)),
            activate(n__s(X)) -> s(activate(X)),
  activate(n__filter(X1, X2)) -> filter(activate(X1), activate(X2)),
    activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
        activate(n__sieve(X)) -> sieve(activate(X)),
             tail(cons(X, Y)) -> activate(Y),
             if(true(), X, Y) -> activate(X),
            if(false(), X, Y) -> activate(Y),
               filter(X1, X2) -> n__filter(X1, X2),
  filter(s(s(X)), cons(Y, Z)) ->
  if(
    divides(s(s(X)), Y), n__filter(n__s(n__s(X)), activate(Z)),
    n__cons(Y, n__filter(X, n__sieve(Y)))
  )
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                       sieve(X) -> n__sieve(X),
              sieve(cons(X, Y)) ->
    cons(X, n__filter(X, n__sieve(activate(Y)))),
                        from(X) -> cons(X, n__from(n__s(X))),
                        from(X) -> n__from(X),
                           s(X) -> n__s(X),
                       primes() -> sieve(from(s(s(0())))),
                   cons(X1, X2) -> n__cons(X1, X2),
               head(cons(X, Y)) -> X,
                    activate(X) -> X,
           activate(n__from(X)) -> from(activate(X)),
              activate(n__s(X)) -> s(activate(X)),
    activate(n__filter(X1, X2)) -> filter(activate(X1), activate(X2)),
      activate(n__cons(X1, X2)) -> cons(activate(X1), X2),
          activate(n__sieve(X)) -> sieve(activate(X)),
               tail(cons(X, Y)) -> activate(Y),
               if(true(), X, Y) -> activate(X),
              if(false(), X, Y) -> activate(Y),
                 filter(X1, X2) -> n__filter(X1, X2),
    filter(s(s(X)), cons(Y, Z)) ->
    if(
      divides(s(s(X)), Y), n__filter(n__s(n__s(X)), activate(Z)),
      n__cons(Y, n__filter(X, n__sieve(Y)))
    )
   }
  Fail