YES
TRS:
 {         a__filter(X1, X2, X3) -> filter(X1, X2, X3),
   a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)),
  a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)),
              mark(cons(X1, X2)) -> cons(mark(X1), X2),
                       mark(0()) -> 0(),
        mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)),
                      mark(s(X)) -> s(mark(X)),
                  mark(sieve(X)) -> a__sieve(mark(X)),
                   mark(nats(X)) -> a__nats(mark(X)),
                 mark(zprimes()) -> a__zprimes(),
                     a__sieve(X) -> sieve(X),
          a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)),
         a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))),
                      a__nats(X) -> nats(X),
                      a__nats(N) -> cons(mark(N), nats(s(N))),
                    a__zprimes() -> a__sieve(a__nats(s(s(0())))),
                    a__zprimes() -> zprimes()}
 DP:
  Strict:
   {a__filter#(cons(X, Y), s(N), M) -> mark#(X),
                mark#(cons(X1, X2)) -> mark#(X1),
          mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)),
          mark#(filter(X1, X2, X3)) -> mark#(X1),
          mark#(filter(X1, X2, X3)) -> mark#(X2),
          mark#(filter(X1, X2, X3)) -> mark#(X3),
                        mark#(s(X)) -> mark#(X),
                    mark#(sieve(X)) -> mark#(X),
                    mark#(sieve(X)) -> a__sieve#(mark(X)),
                     mark#(nats(X)) -> mark#(X),
                     mark#(nats(X)) -> a__nats#(mark(X)),
                   mark#(zprimes()) -> a__zprimes#(),
           a__sieve#(cons(s(N), Y)) -> mark#(N),
                        a__nats#(N) -> mark#(N),
                      a__zprimes#() -> a__sieve#(a__nats(s(s(0())))),
                      a__zprimes#() -> a__nats#(s(s(0())))}
  Weak:
  {         a__filter(X1, X2, X3) -> filter(X1, X2, X3),
    a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)),
   a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)),
               mark(cons(X1, X2)) -> cons(mark(X1), X2),
                        mark(0()) -> 0(),
         mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)),
                       mark(s(X)) -> s(mark(X)),
                   mark(sieve(X)) -> a__sieve(mark(X)),
                    mark(nats(X)) -> a__nats(mark(X)),
                  mark(zprimes()) -> a__zprimes(),
                      a__sieve(X) -> sieve(X),
           a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)),
          a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))),
                       a__nats(X) -> nats(X),
                       a__nats(N) -> cons(mark(N), nats(s(N))),
                     a__zprimes() -> a__sieve(a__nats(s(s(0())))),
                     a__zprimes() -> zprimes()}
  EDG:
   {(mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(zprimes()) -> a__zprimes#())
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(nats(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(sieve(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(s(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(filter(X1, X2, X3)) -> mark#(X1), mark#(cons(X1, X2)) -> mark#(X1))
    (mark#(nats(X)) -> a__nats#(mark(X)), a__nats#(N) -> mark#(N))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(zprimes()) -> a__zprimes#())
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(nats(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(sieve(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(s(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(filter(X1, X2, X3)) -> mark#(X2), mark#(cons(X1, X2)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(zprimes()) -> a__zprimes#())
    (mark#(s(X)) -> mark#(X), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(s(X)) -> mark#(X), mark#(nats(X)) -> mark#(X))
    (mark#(s(X)) -> mark#(X), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(s(X)) -> mark#(X), mark#(sieve(X)) -> mark#(X))
    (mark#(s(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
    (mark#(s(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(s(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(s(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(s(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(s(X)) -> mark#(X), mark#(cons(X1, X2)) -> mark#(X1))
    (mark#(nats(X)) -> mark#(X), mark#(zprimes()) -> a__zprimes#())
    (mark#(nats(X)) -> mark#(X), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(nats(X)) -> mark#(X), mark#(nats(X)) -> mark#(X))
    (mark#(nats(X)) -> mark#(X), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(nats(X)) -> mark#(X), mark#(sieve(X)) -> mark#(X))
    (mark#(nats(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
    (mark#(nats(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(nats(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(nats(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(nats(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(nats(X)) -> mark#(X), mark#(cons(X1, X2)) -> mark#(X1))
    (a__zprimes#() -> a__sieve#(a__nats(s(s(0())))), a__sieve#(cons(s(N), Y)) -> mark#(N))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(zprimes()) -> a__zprimes#())
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(nats(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(sieve(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(s(X)) -> mark#(X))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(filter(X1, X2, X3)) -> mark#(X3), mark#(cons(X1, X2)) -> mark#(X1))
    (a__nats#(N) -> mark#(N), mark#(zprimes()) -> a__zprimes#())
    (a__nats#(N) -> mark#(N), mark#(nats(X)) -> a__nats#(mark(X)))
    (a__nats#(N) -> mark#(N), mark#(nats(X)) -> mark#(X))
    (a__nats#(N) -> mark#(N), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (a__nats#(N) -> mark#(N), mark#(sieve(X)) -> mark#(X))
    (a__nats#(N) -> mark#(N), mark#(s(X)) -> mark#(X))
    (a__nats#(N) -> mark#(N), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (a__nats#(N) -> mark#(N), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (a__nats#(N) -> mark#(N), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (a__nats#(N) -> mark#(N), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (a__nats#(N) -> mark#(N), mark#(cons(X1, X2)) -> mark#(X1))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(cons(X1, X2)) -> mark#(X1))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(s(X)) -> mark#(X))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(sieve(X)) -> mark#(X))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(nats(X)) -> mark#(X))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(nats(X)) -> a__nats#(mark(X)))
    (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(zprimes()) -> a__zprimes#())
    (a__zprimes#() -> a__nats#(s(s(0()))), a__nats#(N) -> mark#(N))
    (mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)), a__filter#(cons(X, Y), s(N), M) -> mark#(X))
    (mark#(sieve(X)) -> mark#(X), mark#(cons(X1, X2)) -> mark#(X1))
    (mark#(sieve(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(sieve(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(sieve(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(sieve(X)) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(sieve(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
    (mark#(sieve(X)) -> mark#(X), mark#(sieve(X)) -> mark#(X))
    (mark#(sieve(X)) -> mark#(X), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(sieve(X)) -> mark#(X), mark#(nats(X)) -> mark#(X))
    (mark#(sieve(X)) -> mark#(X), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(sieve(X)) -> mark#(X), mark#(zprimes()) -> a__zprimes#())
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(cons(X1, X2)) -> mark#(X1))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(s(X)) -> mark#(X))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(sieve(X)) -> mark#(X))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(nats(X)) -> mark#(X))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(nats(X)) -> a__nats#(mark(X)))
    (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(zprimes()) -> a__zprimes#())
    (mark#(zprimes()) -> a__zprimes#(), a__zprimes#() -> a__sieve#(a__nats(s(s(0())))))
    (mark#(zprimes()) -> a__zprimes#(), a__zprimes#() -> a__nats#(s(s(0()))))
    (mark#(sieve(X)) -> a__sieve#(mark(X)), a__sieve#(cons(s(N), Y)) -> mark#(N))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(cons(X1, X2)) -> mark#(X1))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> mark#(X1))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> mark#(X2))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(filter(X1, X2, X3)) -> mark#(X3))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(s(X)) -> mark#(X))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(sieve(X)) -> mark#(X))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(sieve(X)) -> a__sieve#(mark(X)))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(nats(X)) -> mark#(X))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(nats(X)) -> a__nats#(mark(X)))
    (mark#(cons(X1, X2)) -> mark#(X1), mark#(zprimes()) -> a__zprimes#())}
   SCCS:
    Scc:
     {a__filter#(cons(X, Y), s(N), M) -> mark#(X),
                  mark#(cons(X1, X2)) -> mark#(X1),
            mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)),
            mark#(filter(X1, X2, X3)) -> mark#(X1),
            mark#(filter(X1, X2, X3)) -> mark#(X2),
            mark#(filter(X1, X2, X3)) -> mark#(X3),
                          mark#(s(X)) -> mark#(X),
                      mark#(sieve(X)) -> mark#(X),
                      mark#(sieve(X)) -> a__sieve#(mark(X)),
                       mark#(nats(X)) -> mark#(X),
                       mark#(nats(X)) -> a__nats#(mark(X)),
                     mark#(zprimes()) -> a__zprimes#(),
             a__sieve#(cons(s(N), Y)) -> mark#(N),
                          a__nats#(N) -> mark#(N),
                        a__zprimes#() -> a__sieve#(a__nats(s(s(0())))),
                        a__zprimes#() -> a__nats#(s(s(0())))}
    SCC:
     Strict:
      {a__filter#(cons(X, Y), s(N), M) -> mark#(X),
                   mark#(cons(X1, X2)) -> mark#(X1),
             mark#(filter(X1, X2, X3)) -> a__filter#(mark(X1), mark(X2), mark(X3)),
             mark#(filter(X1, X2, X3)) -> mark#(X1),
             mark#(filter(X1, X2, X3)) -> mark#(X2),
             mark#(filter(X1, X2, X3)) -> mark#(X3),
                           mark#(s(X)) -> mark#(X),
                       mark#(sieve(X)) -> mark#(X),
                       mark#(sieve(X)) -> a__sieve#(mark(X)),
                        mark#(nats(X)) -> mark#(X),
                        mark#(nats(X)) -> a__nats#(mark(X)),
                      mark#(zprimes()) -> a__zprimes#(),
              a__sieve#(cons(s(N), Y)) -> mark#(N),
                           a__nats#(N) -> mark#(N),
                         a__zprimes#() -> a__sieve#(a__nats(s(s(0())))),
                         a__zprimes#() -> a__nats#(s(s(0())))}
     Weak:
     {         a__filter(X1, X2, X3) -> filter(X1, X2, X3),
       a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)),
      a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)),
                  mark(cons(X1, X2)) -> cons(mark(X1), X2),
                           mark(0()) -> 0(),
            mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)),
                          mark(s(X)) -> s(mark(X)),
                      mark(sieve(X)) -> a__sieve(mark(X)),
                       mark(nats(X)) -> a__nats(mark(X)),
                     mark(zprimes()) -> a__zprimes(),
                         a__sieve(X) -> sieve(X),
              a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)),
             a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))),
                          a__nats(X) -> nats(X),
                          a__nats(N) -> cons(mark(N), nats(s(N))),
                        a__zprimes() -> a__sieve(a__nats(s(s(0())))),
                        a__zprimes() -> zprimes()}
     POLY:
      Argument Filtering:
       pi(zprimes) = [], pi(a__zprimes#) = [], pi(a__zprimes) = [], pi(a__nats#) = [0], pi(a__nats) = [0], pi(nats) = [0], pi(a__sieve#) = 0, pi(a__sieve) = 0, pi(sieve) = 0, pi(s) = 0, pi(mark#) = [0], pi(mark) = 0, pi(a__filter#) = 0, pi(a__filter) = [0,1,2], pi(filter) = [0,1,2], pi(0) = [], pi(cons) = [0]
      Usable Rules:
       {}
      Interpretation:
       [a__nats#](x0) = x0 + 1,
       [mark#](x0) = x0 + 1,
       [a__zprimes#] = 1,
       [filter](x0, x1, x2) = x0 + x1 + x2 + 1,
       [cons](x0) = x0 + 1,
       [a__nats](x0) = x0 + 1,
       [nats](x0) = x0 + 1,
       [zprimes] = 1,
       [0] = 0
      Strict:
       {a__filter#(cons(X, Y), s(N), M) -> mark#(X),
                            mark#(s(X)) -> mark#(X),
                        mark#(sieve(X)) -> mark#(X),
               a__sieve#(cons(s(N), Y)) -> mark#(N),
                            a__nats#(N) -> mark#(N),
                          a__zprimes#() -> a__sieve#(a__nats(s(s(0())))),
                          a__zprimes#() -> a__nats#(s(s(0())))}
      Weak:
       {         a__filter(X1, X2, X3) -> filter(X1, X2, X3),
         a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)),
        a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)),
                    mark(cons(X1, X2)) -> cons(mark(X1), X2),
                             mark(0()) -> 0(),
              mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)),
                            mark(s(X)) -> s(mark(X)),
                        mark(sieve(X)) -> a__sieve(mark(X)),
                         mark(nats(X)) -> a__nats(mark(X)),
                       mark(zprimes()) -> a__zprimes(),
                           a__sieve(X) -> sieve(X),
                a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)),
               a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))),
                            a__nats(X) -> nats(X),
                            a__nats(N) -> cons(mark(N), nats(s(N))),
                          a__zprimes() -> a__sieve(a__nats(s(s(0())))),
                          a__zprimes() -> zprimes()}
      EDG:
       {(a__nats#(N) -> mark#(N), mark#(sieve(X)) -> mark#(X))
        (a__nats#(N) -> mark#(N), mark#(s(X)) -> mark#(X))
        (mark#(s(X)) -> mark#(X), mark#(sieve(X)) -> mark#(X))
        (mark#(s(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
        (a__zprimes#() -> a__sieve#(a__nats(s(s(0())))), a__sieve#(cons(s(N), Y)) -> mark#(N))
        (a__zprimes#() -> a__nats#(s(s(0()))), a__nats#(N) -> mark#(N))
        (mark#(sieve(X)) -> mark#(X), mark#(s(X)) -> mark#(X))
        (mark#(sieve(X)) -> mark#(X), mark#(sieve(X)) -> mark#(X))
        (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(s(X)) -> mark#(X))
        (a__filter#(cons(X, Y), s(N), M) -> mark#(X), mark#(sieve(X)) -> mark#(X))
        (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(s(X)) -> mark#(X))
        (a__sieve#(cons(s(N), Y)) -> mark#(N), mark#(sieve(X)) -> mark#(X))}
       SCCS:
        Scc:
         {    mark#(s(X)) -> mark#(X),
          mark#(sieve(X)) -> mark#(X)}
        SCC:
         Strict:
          {    mark#(s(X)) -> mark#(X),
           mark#(sieve(X)) -> mark#(X)}
         Weak:
         {         a__filter(X1, X2, X3) -> filter(X1, X2, X3),
           a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)),
          a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)),
                      mark(cons(X1, X2)) -> cons(mark(X1), X2),
                               mark(0()) -> 0(),
                mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)),
                              mark(s(X)) -> s(mark(X)),
                          mark(sieve(X)) -> a__sieve(mark(X)),
                           mark(nats(X)) -> a__nats(mark(X)),
                         mark(zprimes()) -> a__zprimes(),
                             a__sieve(X) -> sieve(X),
                  a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)),
                 a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))),
                              a__nats(X) -> nats(X),
                              a__nats(N) -> cons(mark(N), nats(s(N))),
                            a__zprimes() -> a__sieve(a__nats(s(s(0())))),
                            a__zprimes() -> zprimes()}
         SPSC:
          Simple Projection:
           pi(mark#) = 0
          Strict:
           {mark#(sieve(X)) -> mark#(X)}
          EDG:
           {(mark#(sieve(X)) -> mark#(X), mark#(sieve(X)) -> mark#(X))}
           SCCS:
            Scc:
             {mark#(sieve(X)) -> mark#(X)}
            SCC:
             Strict:
              {mark#(sieve(X)) -> mark#(X)}
             Weak:
             {         a__filter(X1, X2, X3) -> filter(X1, X2, X3),
               a__filter(cons(X, Y), 0(), M) -> cons(0(), filter(Y, M, M)),
              a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)),
                          mark(cons(X1, X2)) -> cons(mark(X1), X2),
                                   mark(0()) -> 0(),
                    mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)),
                                  mark(s(X)) -> s(mark(X)),
                              mark(sieve(X)) -> a__sieve(mark(X)),
                               mark(nats(X)) -> a__nats(mark(X)),
                             mark(zprimes()) -> a__zprimes(),
                                 a__sieve(X) -> sieve(X),
                      a__sieve(cons(0(), Y)) -> cons(0(), sieve(Y)),
                     a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))),
                                  a__nats(X) -> nats(X),
                                  a__nats(N) -> cons(mark(N), nats(s(N))),
                                a__zprimes() -> a__sieve(a__nats(s(s(0())))),
                                a__zprimes() -> zprimes()}
             SPSC:
              Simple Projection:
               pi(mark#) = 0
              Strict:
               {}
              Qed