YES

Problem:
 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))
 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(N) -> cons(mark(N),nats(s(N)))
 a__zprimes() -> a__sieve(a__nats(s(s(0()))))
 mark(filter(X1,X2,X3)) -> a__filter(mark(X1),mark(X2),mark(X3))
 mark(sieve(X)) -> a__sieve(mark(X))
 mark(nats(X)) -> a__nats(mark(X))
 mark(zprimes()) -> a__zprimes()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 a__filter(X1,X2,X3) -> filter(X1,X2,X3)
 a__sieve(X) -> sieve(X)
 a__nats(X) -> nats(X)
 a__zprimes() -> zprimes()

Proof:
 DP Processor:
  DPs:
   a__filter#(cons(X,Y),s(N),M) -> mark#(X)
   a__sieve#(cons(s(N),Y)) -> mark#(N)
   a__nats#(N) -> mark#(N)
   a__zprimes#() -> a__nats#(s(s(0())))
   a__zprimes#() -> a__sieve#(a__nats(s(s(0()))))
   mark#(filter(X1,X2,X3)) -> mark#(X3)
   mark#(filter(X1,X2,X3)) -> mark#(X2)
   mark#(filter(X1,X2,X3)) -> mark#(X1)
   mark#(filter(X1,X2,X3)) -> a__filter#(mark(X1),mark(X2),mark(X3))
   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#()
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   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))
   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(N) -> cons(mark(N),nats(s(N)))
   a__zprimes() -> a__sieve(a__nats(s(s(0()))))
   mark(filter(X1,X2,X3)) -> a__filter(mark(X1),mark(X2),mark(X3))
   mark(sieve(X)) -> a__sieve(mark(X))
   mark(nats(X)) -> a__nats(mark(X))
   mark(zprimes()) -> a__zprimes()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(0()) -> 0()
   mark(s(X)) -> s(mark(X))
   a__filter(X1,X2,X3) -> filter(X1,X2,X3)
   a__sieve(X) -> sieve(X)
   a__nats(X) -> nats(X)
   a__zprimes() -> zprimes()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a__zprimes#] = 7,
    
    [a__nats#](x0) = 2x0 + 1,
    
    [a__sieve#](x0) = x0,
    
    [mark#](x0) = 2x0,
    
    [a__filter#](x0, x1, x2) = 4x0 + 2x1 + 2x2,
    
    [zprimes] = 7,
    
    [a__zprimes] = 7,
    
    [nats](x0) = 2x0 + 2,
    
    [a__nats](x0) = 2x0 + 2,
    
    [sieve](x0) = x0 + 1,
    
    [a__sieve](x0) = x0 + 1,
    
    [mark](x0) = x0,
    
    [s](x0) = x0 + 1,
    
    [filter](x0, x1, x2) = 4x0 + x1 + x2 + 4,
    
    [a__filter](x0, x1, x2) = 4x0 + x1 + x2 + 4,
    
    [0] = 0,
    
    [cons](x0, x1) = 2x0 + 1
   orientation:
    a__filter#(cons(X,Y),s(N),M) = 2M + 2N + 8X + 6 >= 2X = mark#(X)
    
    a__sieve#(cons(s(N),Y)) = 2N + 3 >= 2N = mark#(N)
    
    a__nats#(N) = 2N + 1 >= 2N = mark#(N)
    
    a__zprimes#() = 7 >= 5 = a__nats#(s(s(0())))
    
    a__zprimes#() = 7 >= 6 = a__sieve#(a__nats(s(s(0()))))
    
    mark#(filter(X1,X2,X3)) = 8X1 + 2X2 + 2X3 + 8 >= 2X3 = mark#(X3)
    
    mark#(filter(X1,X2,X3)) = 8X1 + 2X2 + 2X3 + 8 >= 2X2 = mark#(X2)
    
    mark#(filter(X1,X2,X3)) = 8X1 + 2X2 + 2X3 + 8 >= 2X1 = mark#(X1)
    
    mark#(filter(X1,X2,X3)) = 8X1 + 2X2 + 2X3 + 8 >= 4X1 + 2X2 + 2X3 = a__filter#(mark(X1),mark(X2),mark(X3))
    
    mark#(sieve(X)) = 2X + 2 >= 2X = mark#(X)
    
    mark#(sieve(X)) = 2X + 2 >= X = a__sieve#(mark(X))
    
    mark#(nats(X)) = 4X + 4 >= 2X = mark#(X)
    
    mark#(nats(X)) = 4X + 4 >= 2X + 1 = a__nats#(mark(X))
    
    mark#(zprimes()) = 14 >= 7 = a__zprimes#()
    
    mark#(cons(X1,X2)) = 4X1 + 2 >= 2X1 = mark#(X1)
    
    mark#(s(X)) = 2X + 2 >= 2X = mark#(X)
    
    a__filter(cons(X,Y),0(),M) = M + 8X + 8 >= 1 = cons(0(),filter(Y,M,M))
    
    a__filter(cons(X,Y),s(N),M) = M + N + 8X + 9 >= 2X + 1 = cons(mark(X),filter(Y,N,M))
    
    a__sieve(cons(0(),Y)) = 2 >= 1 = cons(0(),sieve(Y))
    
    a__sieve(cons(s(N),Y)) = 2N + 4 >= 2N + 3 = cons(s(mark(N)),sieve(filter(Y,N,N)))
    
    a__nats(N) = 2N + 2 >= 2N + 1 = cons(mark(N),nats(s(N)))
    
    a__zprimes() = 7 >= 7 = a__sieve(a__nats(s(s(0()))))
    
    mark(filter(X1,X2,X3)) = 4X1 + X2 + X3 + 4 >= 4X1 + X2 + X3 + 4 = a__filter(mark(X1),mark(X2),mark(X3))
    
    mark(sieve(X)) = X + 1 >= X + 1 = a__sieve(mark(X))
    
    mark(nats(X)) = 2X + 2 >= 2X + 2 = a__nats(mark(X))
    
    mark(zprimes()) = 7 >= 7 = a__zprimes()
    
    mark(cons(X1,X2)) = 2X1 + 1 >= 2X1 + 1 = cons(mark(X1),X2)
    
    mark(0()) = 0 >= 0 = 0()
    
    mark(s(X)) = X + 1 >= X + 1 = s(mark(X))
    
    a__filter(X1,X2,X3) = 4X1 + X2 + X3 + 4 >= 4X1 + X2 + X3 + 4 = filter(X1,X2,X3)
    
    a__sieve(X) = X + 1 >= X + 1 = sieve(X)
    
    a__nats(X) = 2X + 2 >= 2X + 2 = nats(X)
    
    a__zprimes() = 7 >= 7 = zprimes()
   problem:
    DPs:
     
    TRS:
     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))
     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(N) -> cons(mark(N),nats(s(N)))
     a__zprimes() -> a__sieve(a__nats(s(s(0()))))
     mark(filter(X1,X2,X3)) -> a__filter(mark(X1),mark(X2),mark(X3))
     mark(sieve(X)) -> a__sieve(mark(X))
     mark(nats(X)) -> a__nats(mark(X))
     mark(zprimes()) -> a__zprimes()
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     a__filter(X1,X2,X3) -> filter(X1,X2,X3)
     a__sieve(X) -> sieve(X)
     a__nats(X) -> nats(X)
     a__zprimes() -> zprimes()
   Qed