MAYBE

Problem:
 a__primes() -> a__sieve(a__from(s(s(0()))))
 a__from(X) -> cons(mark(X),from(s(X)))
 a__head(cons(X,Y)) -> mark(X)
 a__tail(cons(X,Y)) -> mark(Y)
 a__if(true(),X,Y) -> mark(X)
 a__if(false(),X,Y) -> mark(Y)
 a__filter(s(s(X)),cons(Y,Z)) ->
 a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
 a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
 mark(primes()) -> a__primes()
 mark(sieve(X)) -> a__sieve(mark(X))
 mark(from(X)) -> a__from(mark(X))
 mark(head(X)) -> a__head(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
 mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
 mark(s(X)) -> s(mark(X))
 mark(0()) -> 0()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(true()) -> true()
 mark(false()) -> false()
 mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
 a__primes() -> primes()
 a__sieve(X) -> sieve(X)
 a__from(X) -> from(X)
 a__head(X) -> head(X)
 a__tail(X) -> tail(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 a__filter(X1,X2) -> filter(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__primes#() -> a__from#(s(s(0())))
   a__primes#() -> a__sieve#(a__from(s(s(0()))))
   a__from#(X) -> mark#(X)
   a__head#(cons(X,Y)) -> mark#(X)
   a__tail#(cons(X,Y)) -> mark#(Y)
   a__if#(true(),X,Y) -> mark#(X)
   a__if#(false(),X,Y) -> mark#(Y)
   a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y)
   a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X)
   a__filter#(s(s(X)),cons(Y,Z)) ->
   a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
   a__sieve#(cons(X,Y)) -> mark#(X)
   mark#(primes()) -> a__primes#()
   mark#(sieve(X)) -> mark#(X)
   mark#(sieve(X)) -> a__sieve#(mark(X))
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(head(X)) -> mark#(X)
   mark#(head(X)) -> a__head#(mark(X))
   mark#(tail(X)) -> mark#(X)
   mark#(tail(X)) -> a__tail#(mark(X))
   mark#(if(X1,X2,X3)) -> mark#(X1)
   mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
   mark#(filter(X1,X2)) -> mark#(X2)
   mark#(filter(X1,X2)) -> mark#(X1)
   mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
   mark#(s(X)) -> mark#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(divides(X1,X2)) -> mark#(X2)
   mark#(divides(X1,X2)) -> mark#(X1)
  TRS:
   a__primes() -> a__sieve(a__from(s(s(0()))))
   a__from(X) -> cons(mark(X),from(s(X)))
   a__head(cons(X,Y)) -> mark(X)
   a__tail(cons(X,Y)) -> mark(Y)
   a__if(true(),X,Y) -> mark(X)
   a__if(false(),X,Y) -> mark(Y)
   a__filter(s(s(X)),cons(Y,Z)) ->
   a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
   a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
   mark(primes()) -> a__primes()
   mark(sieve(X)) -> a__sieve(mark(X))
   mark(from(X)) -> a__from(mark(X))
   mark(head(X)) -> a__head(mark(X))
   mark(tail(X)) -> a__tail(mark(X))
   mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
   mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
   mark(s(X)) -> s(mark(X))
   mark(0()) -> 0()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(true()) -> true()
   mark(false()) -> false()
   mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
   a__primes() -> primes()
   a__sieve(X) -> sieve(X)
   a__from(X) -> from(X)
   a__head(X) -> head(X)
   a__tail(X) -> tail(X)
   a__if(X1,X2,X3) -> if(X1,X2,X3)
   a__filter(X1,X2) -> filter(X1,X2)
  TDG Processor:
   DPs:
    a__primes#() -> a__from#(s(s(0())))
    a__primes#() -> a__sieve#(a__from(s(s(0()))))
    a__from#(X) -> mark#(X)
    a__head#(cons(X,Y)) -> mark#(X)
    a__tail#(cons(X,Y)) -> mark#(Y)
    a__if#(true(),X,Y) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) ->
    a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    a__sieve#(cons(X,Y)) -> mark#(X)
    mark#(primes()) -> a__primes#()
    mark#(sieve(X)) -> mark#(X)
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X))
    mark#(head(X)) -> mark#(X)
    mark#(head(X)) -> a__head#(mark(X))
    mark#(tail(X)) -> mark#(X)
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(divides(X1,X2)) -> mark#(X1)
   TRS:
    a__primes() -> a__sieve(a__from(s(s(0()))))
    a__from(X) -> cons(mark(X),from(s(X)))
    a__head(cons(X,Y)) -> mark(X)
    a__tail(cons(X,Y)) -> mark(Y)
    a__if(true(),X,Y) -> mark(X)
    a__if(false(),X,Y) -> mark(Y)
    a__filter(s(s(X)),cons(Y,Z)) ->
    a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
    mark(primes()) -> a__primes()
    mark(sieve(X)) -> a__sieve(mark(X))
    mark(from(X)) -> a__from(mark(X))
    mark(head(X)) -> a__head(mark(X))
    mark(tail(X)) -> a__tail(mark(X))
    mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
    mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
    mark(s(X)) -> s(mark(X))
    mark(0()) -> 0()
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(true()) -> true()
    mark(false()) -> false()
    mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
    a__primes() -> primes()
    a__sieve(X) -> sieve(X)
    a__from(X) -> from(X)
    a__head(X) -> head(X)
    a__tail(X) -> tail(X)
    a__if(X1,X2,X3) -> if(X1,X2,X3)
    a__filter(X1,X2) -> filter(X1,X2)
   graph:
    a__filter#(s(s(X)),cons(Y,Z)) ->
    a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) ->
    a__if#(false(),X,Y) -> mark#(Y)
    a__filter#(s(s(X)),cons(Y,Z)) ->
    a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) ->
    a__if#(true(),X,Y) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(s(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(tail(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(head(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(from(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(sieve(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
    mark#(primes()) -> a__primes#()
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(s(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(tail(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(head(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(from(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(sieve(X)) -> mark#(X)
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(s(X)) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(tail(X)) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(head(X)) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(from(X)) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__if#(false(),X,Y) -> mark#(Y) -> mark#(sieve(X)) -> mark#(X)
    a__if#(false(),X,Y) -> mark#(Y) ->
    mark#(primes()) -> a__primes#()
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__if#(true(),X,Y) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__if#(true(),X,Y) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__if#(true(),X,Y) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__if#(true(),X,Y) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__if#(true(),X,Y) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    a__if#(true(),X,Y) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(s(X)) -> mark#(X)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(tail(X)) -> mark#(X)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(head(X)) -> mark#(X)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(from(X)) -> mark#(X)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(sieve(X)) -> mark#(X)
    a__tail#(cons(X,Y)) -> mark#(Y) ->
    mark#(primes()) -> a__primes#()
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__head#(cons(X,Y)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__head#(cons(X,Y)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__head#(cons(X,Y)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__head#(cons(X,Y)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__head#(cons(X,Y)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    a__head#(cons(X,Y)) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3) ->
    a__if#(false(),X,Y) -> mark#(Y)
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3) ->
    a__if#(true(),X,Y) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(tail(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(head(X)) -> a__head#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(head(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(sieve(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(primes()) -> a__primes#()
    mark#(tail(X)) -> a__tail#(mark(X)) ->
    a__tail#(cons(X,Y)) -> mark#(Y)
    mark#(tail(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
    mark#(tail(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
    mark#(tail(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(tail(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(tail(X)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(tail(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
    mark#(tail(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
    mark#(tail(X)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(tail(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(tail(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    mark#(tail(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    mark#(tail(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
    mark#(tail(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    mark#(tail(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(tail(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(tail(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(tail(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    mark#(tail(X)) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    mark#(head(X)) -> a__head#(mark(X)) ->
    a__head#(cons(X,Y)) -> mark#(X)
    mark#(head(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
    mark#(head(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
    mark#(head(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(head(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(head(X)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(head(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
    mark#(head(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
    mark#(head(X)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(head(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(head(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    mark#(head(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    mark#(head(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
    mark#(head(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    mark#(head(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(head(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(head(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(head(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    mark#(head(X)) -> mark#(X) -> mark#(primes()) -> a__primes#()
    mark#(primes()) -> a__primes#() ->
    a__primes#() -> a__sieve#(a__from(s(s(0()))))
    mark#(primes()) -> a__primes#() ->
    a__primes#() -> a__from#(s(s(0())))
    mark#(sieve(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
    mark#(sieve(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
    mark#(sieve(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(sieve(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(sieve(X)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(sieve(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
    mark#(sieve(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
    mark#(sieve(X)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(sieve(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(sieve(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    mark#(sieve(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    mark#(sieve(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
    mark#(sieve(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    mark#(sieve(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(sieve(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(sieve(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(sieve(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    mark#(sieve(X)) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    mark#(sieve(X)) -> a__sieve#(mark(X)) ->
    a__sieve#(cons(X,Y)) -> mark#(X)
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2)) ->
    a__filter#(s(s(X)),cons(Y,Z)) ->
    a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2)) ->
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X)
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2)) ->
    a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(tail(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(head(X)) -> a__head#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(head(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(from(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(sieve(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X2) ->
    mark#(primes()) -> a__primes#()
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(tail(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(head(X)) -> a__head#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(head(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(sieve(X)) -> mark#(X)
    mark#(filter(X1,X2)) -> mark#(X1) ->
    mark#(primes()) -> a__primes#()
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(tail(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(head(X)) -> a__head#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(head(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(from(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(sieve(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X2) ->
    mark#(primes()) -> a__primes#()
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(tail(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(head(X)) -> a__head#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(head(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(sieve(X)) -> mark#(X)
    mark#(divides(X1,X2)) -> mark#(X1) ->
    mark#(primes()) -> a__primes#()
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(tail(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(head(X)) -> a__head#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(head(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(sieve(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(primes()) -> a__primes#()
    mark#(from(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
    mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(from(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
    mark#(from(X)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(from(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    mark#(s(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(from(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#(primes()) -> a__primes#()
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X1)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(divides(X1,X2)) -> mark#(X2)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X1)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(filter(X1,X2)) -> mark#(X2)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(head(X)) -> a__head#(mark(X))
    a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__sieve#(cons(X,Y)) -> mark#(X) ->
    mark#(sieve(X)) -> a__sieve#(mark(X))
    a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(primes()) -> a__primes#()
    a__from#(X) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
    a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__from#(X) -> mark#(X) ->
    mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
    a__from#(X) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
    a__from#(X) -> mark#(X) -> mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
    a__from#(X) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(head(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
    a__from#(X) -> mark#(X) ->
    mark#(primes()) -> a__primes#()
    a__primes#() -> a__sieve#(a__from(s(s(0())))) ->
    a__sieve#(cons(X,Y)) -> mark#(X)
    a__primes#() -> a__from#(s(s(0()))) -> a__from#(X) -> mark#(X)
   EDG Processor:
    DPs:
     a__primes#() -> a__from#(s(s(0())))
     a__primes#() -> a__sieve#(a__from(s(s(0()))))
     a__from#(X) -> mark#(X)
     a__head#(cons(X,Y)) -> mark#(X)
     a__tail#(cons(X,Y)) -> mark#(Y)
     a__if#(true(),X,Y) -> mark#(X)
     a__if#(false(),X,Y) -> mark#(Y)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) ->
     a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
     a__sieve#(cons(X,Y)) -> mark#(X)
     mark#(primes()) -> a__primes#()
     mark#(sieve(X)) -> mark#(X)
     mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(from(X)) -> mark#(X)
     mark#(from(X)) -> a__from#(mark(X))
     mark#(head(X)) -> mark#(X)
     mark#(head(X)) -> a__head#(mark(X))
     mark#(tail(X)) -> mark#(X)
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(s(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(divides(X1,X2)) -> mark#(X1)
    TRS:
     a__primes() -> a__sieve(a__from(s(s(0()))))
     a__from(X) -> cons(mark(X),from(s(X)))
     a__head(cons(X,Y)) -> mark(X)
     a__tail(cons(X,Y)) -> mark(Y)
     a__if(true(),X,Y) -> mark(X)
     a__if(false(),X,Y) -> mark(Y)
     a__filter(s(s(X)),cons(Y,Z)) ->
     a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
     a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
     mark(primes()) -> a__primes()
     mark(sieve(X)) -> a__sieve(mark(X))
     mark(from(X)) -> a__from(mark(X))
     mark(head(X)) -> a__head(mark(X))
     mark(tail(X)) -> a__tail(mark(X))
     mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
     mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
     mark(s(X)) -> s(mark(X))
     mark(0()) -> 0()
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(true()) -> true()
     mark(false()) -> false()
     mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
     a__primes() -> primes()
     a__sieve(X) -> sieve(X)
     a__from(X) -> from(X)
     a__head(X) -> head(X)
     a__tail(X) -> tail(X)
     a__if(X1,X2,X3) -> if(X1,X2,X3)
     a__filter(X1,X2) -> filter(X1,X2)
    graph:
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(primes()) -> a__primes#()
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(sieve(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(from(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(head(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(tail(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(s(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(primes()) -> a__primes#()
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(sieve(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(from(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(head(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(tail(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(s(X)) -> mark#(X)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(primes()) -> a__primes#()
     a__if#(false(),X,Y) -> mark#(Y) -> mark#(sieve(X)) -> mark#(X)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__if#(false(),X,Y) -> mark#(Y) -> mark#(from(X)) -> mark#(X)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__if#(false(),X,Y) -> mark#(Y) -> mark#(head(X)) -> mark#(X)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__if#(false(),X,Y) -> mark#(Y) -> mark#(tail(X)) -> mark#(X)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__if#(false(),X,Y) -> mark#(Y) -> mark#(s(X)) -> mark#(X)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__if#(false(),X,Y) -> mark#(Y) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(primes()) -> a__primes#()
     a__if#(true(),X,Y) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__if#(true(),X,Y) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__if#(true(),X,Y) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__if#(true(),X,Y) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__if#(true(),X,Y) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__if#(true(),X,Y) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(primes()) -> a__primes#()
     a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(sieve(X)) -> mark#(X)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(from(X)) -> mark#(X)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(head(X)) -> mark#(X)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(tail(X)) -> mark#(X)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__tail#(cons(X,Y)) -> mark#(Y) -> mark#(s(X)) -> mark#(X)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__tail#(cons(X,Y)) -> mark#(Y) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(primes()) -> a__primes#()
     a__head#(cons(X,Y)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__head#(cons(X,Y)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__head#(cons(X,Y)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__head#(cons(X,Y)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__head#(cons(X,Y)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__head#(cons(X,Y)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3) ->
     a__if#(true(),X,Y) -> mark#(X)
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3) ->
     a__if#(false(),X,Y) -> mark#(Y)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(primes()) -> a__primes#()
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(sieve(X)) -> mark#(X)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(from(X)) -> a__from#(mark(X))
     mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(head(X)) -> mark#(X)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(head(X)) -> a__head#(mark(X))
     mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(tail(X)) -> mark#(X)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(if(X1,X2,X3)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(tail(X)) -> a__tail#(mark(X)) ->
     a__tail#(cons(X,Y)) -> mark#(Y)
     mark#(tail(X)) -> mark#(X) -> mark#(primes()) -> a__primes#()
     mark#(tail(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     mark#(tail(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(tail(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     mark#(tail(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
     mark#(tail(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     mark#(tail(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
     mark#(tail(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     mark#(tail(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
     mark#(tail(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(tail(X)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(tail(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
     mark#(tail(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
     mark#(tail(X)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(tail(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     mark#(tail(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
     mark#(tail(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
     mark#(tail(X)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(head(X)) -> a__head#(mark(X)) ->
     a__head#(cons(X,Y)) -> mark#(X)
     mark#(head(X)) -> mark#(X) -> mark#(primes()) -> a__primes#()
     mark#(head(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     mark#(head(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(head(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     mark#(head(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
     mark#(head(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     mark#(head(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
     mark#(head(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     mark#(head(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
     mark#(head(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(head(X)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(head(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
     mark#(head(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
     mark#(head(X)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(head(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     mark#(head(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
     mark#(head(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
     mark#(head(X)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(primes()) -> a__primes#() ->
     a__primes#() -> a__from#(s(s(0())))
     mark#(primes()) -> a__primes#() ->
     a__primes#() -> a__sieve#(a__from(s(s(0()))))
     mark#(sieve(X)) -> mark#(X) -> mark#(primes()) -> a__primes#()
     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#(from(X)) -> mark#(X)
     mark#(sieve(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
     mark#(sieve(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     mark#(sieve(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
     mark#(sieve(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     mark#(sieve(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
     mark#(sieve(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(sieve(X)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(sieve(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
     mark#(sieve(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
     mark#(sieve(X)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(sieve(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     mark#(sieve(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
     mark#(sieve(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
     mark#(sieve(X)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(sieve(X)) -> a__sieve#(mark(X)) ->
     a__sieve#(cons(X,Y)) -> mark#(X)
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2)) ->
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y)
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2)) ->
     a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X)
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2)) ->
     a__filter#(s(s(X)),cons(Y,Z)) ->
     a__if#(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(primes()) -> a__primes#()
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(sieve(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(from(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(from(X)) -> a__from#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(head(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(head(X)) -> a__head#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(tail(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(filter(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(filter(X1,X2)) -> mark#(X2) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(primes()) -> a__primes#()
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(sieve(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(from(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(from(X)) -> a__from#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(head(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(head(X)) -> a__head#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(tail(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(filter(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(filter(X1,X2)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(primes()) -> a__primes#()
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(sieve(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(from(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(from(X)) -> a__from#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(head(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(head(X)) -> a__head#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(tail(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(s(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(divides(X1,X2)) -> mark#(X2) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(primes()) -> a__primes#()
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(sieve(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(from(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(from(X)) -> a__from#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(head(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(head(X)) -> a__head#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(tail(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(s(X)) -> mark#(X)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(divides(X1,X2)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(primes()) -> a__primes#()
     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#(from(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(from(X)) -> a__from#(mark(X))
     mark#(cons(X1,X2)) -> mark#(X1) -> mark#(head(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(head(X)) -> a__head#(mark(X))
     mark#(cons(X1,X2)) -> mark#(X1) -> mark#(tail(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     mark#(cons(X1,X2)) -> mark#(X1) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> mark#(X) -> mark#(primes()) -> a__primes#()
     mark#(from(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     mark#(from(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
     mark#(from(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     mark#(from(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
     mark#(from(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     mark#(from(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
     mark#(from(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(from(X)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(from(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
     mark#(from(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
     mark#(from(X)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X)
     mark#(s(X)) -> mark#(X) -> mark#(primes()) -> a__primes#()
     mark#(s(X)) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     mark#(s(X)) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
     mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
     mark#(s(X)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     mark#(s(X)) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
     mark#(s(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     mark#(s(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
     mark#(s(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(s(X)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     mark#(s(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
     mark#(s(X)) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
     mark#(s(X)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
     mark#(s(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
     mark#(s(X)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(primes()) -> a__primes#()
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(sieve(X)) -> mark#(X)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(sieve(X)) -> a__sieve#(mark(X))
     a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(from(X)) -> a__from#(mark(X))
     a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(head(X)) -> a__head#(mark(X))
     a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(tail(X)) -> a__tail#(mark(X))
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> mark#(X1)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X2)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> mark#(X1)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(cons(X1,X2)) -> mark#(X1)
     a__sieve#(cons(X,Y)) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X2)
     a__sieve#(cons(X,Y)) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X1)
     a__from#(X) -> mark#(X) -> mark#(primes()) -> a__primes#()
     a__from#(X) -> mark#(X) -> mark#(sieve(X)) -> mark#(X)
     a__from#(X) -> mark#(X) -> mark#(sieve(X)) -> a__sieve#(mark(X))
     a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X)
     a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
     a__from#(X) -> mark#(X) -> mark#(head(X)) -> mark#(X)
     a__from#(X) -> mark#(X) -> mark#(head(X)) -> a__head#(mark(X))
     a__from#(X) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
     a__from#(X) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
     a__from#(X) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
     a__from#(X) -> mark#(X) ->
     mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
     a__from#(X) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X2)
     a__from#(X) -> mark#(X) -> mark#(filter(X1,X2)) -> mark#(X1)
     a__from#(X) -> mark#(X) ->
     mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
     a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
     a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
     a__from#(X) -> mark#(X) -> mark#(divides(X1,X2)) -> mark#(X2)
     a__from#(X) -> mark#(X) ->
     mark#(divides(X1,X2)) -> mark#(X1)
     a__primes#() -> a__sieve#(a__from(s(s(0())))) ->
     a__sieve#(cons(X,Y)) -> mark#(X)
     a__primes#() -> a__from#(s(s(0()))) -> a__from#(X) -> mark#(X)
    SCC Processor:
     #sccs: 1
     #rules: 28
     #arcs: 355/841
     DPs:
      a__filter#(s(s(X)),cons(Y,Z)) -> mark#(Y)
      mark#(divides(X1,X2)) -> mark#(X1)
      mark#(divides(X1,X2)) -> mark#(X2)
      mark#(cons(X1,X2)) -> mark#(X1)
      mark#(s(X)) -> mark#(X)
      mark#(filter(X1,X2)) -> a__filter#(mark(X1),mark(X2))
      a__filter#(s(s(X)),cons(Y,Z)) -> mark#(X)
      mark#(filter(X1,X2)) -> mark#(X1)
      mark#(filter(X1,X2)) -> mark#(X2)
      mark#(if(X1,X2,X3)) -> a__if#(mark(X1),X2,X3)
      a__if#(false(),X,Y) -> mark#(Y)
      mark#(if(X1,X2,X3)) -> mark#(X1)
      mark#(tail(X)) -> a__tail#(mark(X))
      a__tail#(cons(X,Y)) -> mark#(Y)
      mark#(tail(X)) -> mark#(X)
      mark#(head(X)) -> a__head#(mark(X))
      a__head#(cons(X,Y)) -> mark#(X)
      mark#(head(X)) -> mark#(X)
      mark#(from(X)) -> a__from#(mark(X))
      a__from#(X) -> mark#(X)
      mark#(from(X)) -> mark#(X)
      mark#(sieve(X)) -> a__sieve#(mark(X))
      a__sieve#(cons(X,Y)) -> mark#(X)
      mark#(sieve(X)) -> mark#(X)
      mark#(primes()) -> a__primes#()
      a__primes#() -> a__sieve#(a__from(s(s(0()))))
      a__primes#() -> a__from#(s(s(0())))
      a__if#(true(),X,Y) -> mark#(X)
     TRS:
      a__primes() -> a__sieve(a__from(s(s(0()))))
      a__from(X) -> cons(mark(X),from(s(X)))
      a__head(cons(X,Y)) -> mark(X)
      a__tail(cons(X,Y)) -> mark(Y)
      a__if(true(),X,Y) -> mark(X)
      a__if(false(),X,Y) -> mark(Y)
      a__filter(s(s(X)),cons(Y,Z)) ->
      a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
      a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y)))
      mark(primes()) -> a__primes()
      mark(sieve(X)) -> a__sieve(mark(X))
      mark(from(X)) -> a__from(mark(X))
      mark(head(X)) -> a__head(mark(X))
      mark(tail(X)) -> a__tail(mark(X))
      mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
      mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2))
      mark(s(X)) -> s(mark(X))
      mark(0()) -> 0()
      mark(cons(X1,X2)) -> cons(mark(X1),X2)
      mark(true()) -> true()
      mark(false()) -> false()
      mark(divides(X1,X2)) -> divides(mark(X1),mark(X2))
      a__primes() -> primes()
      a__sieve(X) -> sieve(X)
      a__from(X) -> from(X)
      a__head(X) -> head(X)
      a__tail(X) -> tail(X)
      a__if(X1,X2,X3) -> if(X1,X2,X3)
      a__filter(X1,X2) -> filter(X1,X2)
     Open