MAYBE

Problem:
 active(primes()) -> mark(sieve(from(s(s(0())))))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(head(cons(X,Y))) -> mark(X)
 active(tail(cons(X,Y))) -> mark(Y)
 active(if(true(),X,Y)) -> mark(X)
 active(if(false(),X,Y)) -> mark(Y)
 active(filter(s(s(X)),cons(Y,Z))) ->
 mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
 active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
 active(sieve(X)) -> sieve(active(X))
 active(from(X)) -> from(active(X))
 active(s(X)) -> s(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(head(X)) -> head(active(X))
 active(tail(X)) -> tail(active(X))
 active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
 active(filter(X1,X2)) -> filter(active(X1),X2)
 active(filter(X1,X2)) -> filter(X1,active(X2))
 active(divides(X1,X2)) -> divides(active(X1),X2)
 active(divides(X1,X2)) -> divides(X1,active(X2))
 sieve(mark(X)) -> mark(sieve(X))
 from(mark(X)) -> mark(from(X))
 s(mark(X)) -> mark(s(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 head(mark(X)) -> mark(head(X))
 tail(mark(X)) -> mark(tail(X))
 if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
 filter(mark(X1),X2) -> mark(filter(X1,X2))
 filter(X1,mark(X2)) -> mark(filter(X1,X2))
 divides(mark(X1),X2) -> mark(divides(X1,X2))
 divides(X1,mark(X2)) -> mark(divides(X1,X2))
 proper(primes()) -> ok(primes())
 proper(sieve(X)) -> sieve(proper(X))
 proper(from(X)) -> from(proper(X))
 proper(s(X)) -> s(proper(X))
 proper(0()) -> ok(0())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(head(X)) -> head(proper(X))
 proper(tail(X)) -> tail(proper(X))
 proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
 proper(true()) -> ok(true())
 proper(false()) -> ok(false())
 proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
 proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
 sieve(ok(X)) -> ok(sieve(X))
 from(ok(X)) -> ok(from(X))
 s(ok(X)) -> ok(s(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 head(ok(X)) -> ok(head(X))
 tail(ok(X)) -> ok(tail(X))
 if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
 filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
 divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(primes()) -> s#(0())
   active#(primes()) -> s#(s(0()))
   active#(primes()) -> from#(s(s(0())))
   active#(primes()) -> sieve#(from(s(s(0()))))
   active#(from(X)) -> s#(X)
   active#(from(X)) -> from#(s(X))
   active#(from(X)) -> cons#(X,from(s(X)))
   active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
   active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
   active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
   active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
   active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
   active#(filter(s(s(X)),cons(Y,Z))) ->
   if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
   active#(sieve(cons(X,Y))) -> sieve#(Y)
   active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
   active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
   active#(sieve(X)) -> active#(X)
   active#(sieve(X)) -> sieve#(active(X))
   active#(from(X)) -> active#(X)
   active#(from(X)) -> from#(active(X))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(cons(X1,X2)) -> active#(X1)
   active#(cons(X1,X2)) -> cons#(active(X1),X2)
   active#(head(X)) -> active#(X)
   active#(head(X)) -> head#(active(X))
   active#(tail(X)) -> active#(X)
   active#(tail(X)) -> tail#(active(X))
   active#(if(X1,X2,X3)) -> active#(X1)
   active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
   active#(filter(X1,X2)) -> active#(X1)
   active#(filter(X1,X2)) -> filter#(active(X1),X2)
   active#(filter(X1,X2)) -> active#(X2)
   active#(filter(X1,X2)) -> filter#(X1,active(X2))
   active#(divides(X1,X2)) -> active#(X1)
   active#(divides(X1,X2)) -> divides#(active(X1),X2)
   active#(divides(X1,X2)) -> active#(X2)
   active#(divides(X1,X2)) -> divides#(X1,active(X2))
   sieve#(mark(X)) -> sieve#(X)
   from#(mark(X)) -> from#(X)
   s#(mark(X)) -> s#(X)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   head#(mark(X)) -> head#(X)
   tail#(mark(X)) -> tail#(X)
   if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
   filter#(mark(X1),X2) -> filter#(X1,X2)
   filter#(X1,mark(X2)) -> filter#(X1,X2)
   divides#(mark(X1),X2) -> divides#(X1,X2)
   divides#(X1,mark(X2)) -> divides#(X1,X2)
   proper#(sieve(X)) -> proper#(X)
   proper#(sieve(X)) -> sieve#(proper(X))
   proper#(from(X)) -> proper#(X)
   proper#(from(X)) -> from#(proper(X))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(cons(X1,X2)) -> proper#(X2)
   proper#(cons(X1,X2)) -> proper#(X1)
   proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
   proper#(head(X)) -> proper#(X)
   proper#(head(X)) -> head#(proper(X))
   proper#(tail(X)) -> proper#(X)
   proper#(tail(X)) -> tail#(proper(X))
   proper#(if(X1,X2,X3)) -> proper#(X3)
   proper#(if(X1,X2,X3)) -> proper#(X2)
   proper#(if(X1,X2,X3)) -> proper#(X1)
   proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
   proper#(filter(X1,X2)) -> proper#(X2)
   proper#(filter(X1,X2)) -> proper#(X1)
   proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
   proper#(divides(X1,X2)) -> proper#(X2)
   proper#(divides(X1,X2)) -> proper#(X1)
   proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
   sieve#(ok(X)) -> sieve#(X)
   from#(ok(X)) -> from#(X)
   s#(ok(X)) -> s#(X)
   cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
   head#(ok(X)) -> head#(X)
   tail#(ok(X)) -> tail#(X)
   if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
   filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
   divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(primes()) -> mark(sieve(from(s(s(0())))))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(head(cons(X,Y))) -> mark(X)
   active(tail(cons(X,Y))) -> mark(Y)
   active(if(true(),X,Y)) -> mark(X)
   active(if(false(),X,Y)) -> mark(Y)
   active(filter(s(s(X)),cons(Y,Z))) ->
   mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
   active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
   active(sieve(X)) -> sieve(active(X))
   active(from(X)) -> from(active(X))
   active(s(X)) -> s(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(head(X)) -> head(active(X))
   active(tail(X)) -> tail(active(X))
   active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
   active(filter(X1,X2)) -> filter(active(X1),X2)
   active(filter(X1,X2)) -> filter(X1,active(X2))
   active(divides(X1,X2)) -> divides(active(X1),X2)
   active(divides(X1,X2)) -> divides(X1,active(X2))
   sieve(mark(X)) -> mark(sieve(X))
   from(mark(X)) -> mark(from(X))
   s(mark(X)) -> mark(s(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   head(mark(X)) -> mark(head(X))
   tail(mark(X)) -> mark(tail(X))
   if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
   filter(mark(X1),X2) -> mark(filter(X1,X2))
   filter(X1,mark(X2)) -> mark(filter(X1,X2))
   divides(mark(X1),X2) -> mark(divides(X1,X2))
   divides(X1,mark(X2)) -> mark(divides(X1,X2))
   proper(primes()) -> ok(primes())
   proper(sieve(X)) -> sieve(proper(X))
   proper(from(X)) -> from(proper(X))
   proper(s(X)) -> s(proper(X))
   proper(0()) -> ok(0())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(head(X)) -> head(proper(X))
   proper(tail(X)) -> tail(proper(X))
   proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
   proper(true()) -> ok(true())
   proper(false()) -> ok(false())
   proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
   proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
   sieve(ok(X)) -> ok(sieve(X))
   from(ok(X)) -> ok(from(X))
   s(ok(X)) -> ok(s(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   head(ok(X)) -> ok(head(X))
   tail(ok(X)) -> ok(tail(X))
   if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
   filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
   divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  EDG Processor:
   DPs:
    active#(primes()) -> s#(0())
    active#(primes()) -> s#(s(0()))
    active#(primes()) -> from#(s(s(0())))
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(from(X)) -> s#(X)
    active#(from(X)) -> from#(s(X))
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(sieve(X)) -> active#(X)
    active#(sieve(X)) -> sieve#(active(X))
    active#(from(X)) -> active#(X)
    active#(from(X)) -> from#(active(X))
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(head(X)) -> active#(X)
    active#(head(X)) -> head#(active(X))
    active#(tail(X)) -> active#(X)
    active#(tail(X)) -> tail#(active(X))
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(filter(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X2)
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(divides(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X2)
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    sieve#(mark(X)) -> sieve#(X)
    from#(mark(X)) -> from#(X)
    s#(mark(X)) -> s#(X)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    head#(mark(X)) -> head#(X)
    tail#(mark(X)) -> tail#(X)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    filter#(mark(X1),X2) -> filter#(X1,X2)
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    divides#(mark(X1),X2) -> divides#(X1,X2)
    divides#(X1,mark(X2)) -> divides#(X1,X2)
    proper#(sieve(X)) -> proper#(X)
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> from#(proper(X))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(head(X)) -> proper#(X)
    proper#(head(X)) -> head#(proper(X))
    proper#(tail(X)) -> proper#(X)
    proper#(tail(X)) -> tail#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    sieve#(ok(X)) -> sieve#(X)
    from#(ok(X)) -> from#(X)
    s#(ok(X)) -> s#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    head#(ok(X)) -> head#(X)
    tail#(ok(X)) -> tail#(X)
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(primes()) -> mark(sieve(from(s(s(0())))))
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(head(cons(X,Y))) -> mark(X)
    active(tail(cons(X,Y))) -> mark(Y)
    active(if(true(),X,Y)) -> mark(X)
    active(if(false(),X,Y)) -> mark(Y)
    active(filter(s(s(X)),cons(Y,Z))) ->
    mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
    active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
    active(sieve(X)) -> sieve(active(X))
    active(from(X)) -> from(active(X))
    active(s(X)) -> s(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(head(X)) -> head(active(X))
    active(tail(X)) -> tail(active(X))
    active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
    active(filter(X1,X2)) -> filter(active(X1),X2)
    active(filter(X1,X2)) -> filter(X1,active(X2))
    active(divides(X1,X2)) -> divides(active(X1),X2)
    active(divides(X1,X2)) -> divides(X1,active(X2))
    sieve(mark(X)) -> mark(sieve(X))
    from(mark(X)) -> mark(from(X))
    s(mark(X)) -> mark(s(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    head(mark(X)) -> mark(head(X))
    tail(mark(X)) -> mark(tail(X))
    if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
    filter(mark(X1),X2) -> mark(filter(X1,X2))
    filter(X1,mark(X2)) -> mark(filter(X1,X2))
    divides(mark(X1),X2) -> mark(divides(X1,X2))
    divides(X1,mark(X2)) -> mark(divides(X1,X2))
    proper(primes()) -> ok(primes())
    proper(sieve(X)) -> sieve(proper(X))
    proper(from(X)) -> from(proper(X))
    proper(s(X)) -> s(proper(X))
    proper(0()) -> ok(0())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(head(X)) -> head(proper(X))
    proper(tail(X)) -> tail(proper(X))
    proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
    proper(true()) -> ok(true())
    proper(false()) -> ok(false())
    proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
    proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
    sieve(ok(X)) -> ok(sieve(X))
    from(ok(X)) -> ok(from(X))
    s(ok(X)) -> ok(s(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    head(ok(X)) -> ok(head(X))
    tail(ok(X)) -> ok(tail(X))
    if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
    filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
    divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> active#(X) -> active#(primes()) -> s#(0())
    top#(ok(X)) -> active#(X) -> active#(primes()) -> s#(s(0()))
    top#(ok(X)) -> active#(X) -> active#(primes()) -> from#(s(s(0())))
    top#(ok(X)) -> active#(X) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X)))
    top#(ok(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    top#(ok(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    top#(ok(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    top#(ok(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    top#(ok(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    top#(ok(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    top#(ok(X)) -> active#(X) -> active#(sieve(cons(X,Y))) -> sieve#(Y)
    top#(ok(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    top#(ok(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    top#(ok(X)) -> active#(X) -> active#(sieve(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(sieve(X)) -> sieve#(active(X))
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
    top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(head(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(head(X)) -> head#(active(X))
    top#(ok(X)) -> active#(X) -> active#(tail(X)) -> active#(X)
    top#(ok(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X))
    top#(ok(X)) -> active#(X) -> active#(if(X1,X2,X3)) -> active#(X1)
    top#(ok(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    top#(ok(X)) -> active#(X) -> active#(filter(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(filter(X1,X2)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    top#(ok(X)) -> active#(X) -> active#(divides(X1,X2)) -> active#(X1)
    top#(ok(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    top#(ok(X)) -> active#(X) -> active#(divides(X1,X2)) -> active#(X2)
    top#(ok(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> proper#(X) -> proper#(sieve(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(if(X1,X2,X3)) -> proper#(X3)
    top#(mark(X)) -> proper#(X) -> proper#(if(X1,X2,X3)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) -> proper#(if(X1,X2,X3)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    top#(mark(X)) -> proper#(X) -> proper#(filter(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) -> proper#(filter(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    top#(mark(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    top#(mark(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    top#(mark(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(sieve(X)) -> proper#(X)
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    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(head(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(tail(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(sieve(X)) -> proper#(X)
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    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(head(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(tail(X)) -> proper#(X)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(divides(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2)) ->
    divides#(mark(X1),X2) -> divides#(X1,X2)
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2)) ->
    divides#(X1,mark(X2)) -> divides#(X1,X2)
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2)) ->
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(head(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(tail(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
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    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(head(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(tail(X)) -> proper#(X)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(filter(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(filter(X1,X2)) -> proper#(X1) ->
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    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2)) ->
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    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2)) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2)) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(from(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(s(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(head(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(tail(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X3) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
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    proper#(s(X)) -> proper#(X)
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    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
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    proper#(cons(X1,X2)) -> proper#(X1)
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    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(head(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(tail(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(head(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(tail(X)) -> proper#(X)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(if(X1,X2,X3)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3)) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3)) ->
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
    proper#(tail(X)) -> proper#(X) -> proper#(sieve(X)) -> proper#(X)
    proper#(tail(X)) -> proper#(X) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(tail(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(tail(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(tail(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(tail(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(tail(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(tail(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(tail(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(tail(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X)
    proper#(tail(X)) -> proper#(X) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(tail(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X)
    proper#(tail(X)) -> proper#(X) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(tail(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(tail(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(tail(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(tail(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(tail(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(tail(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(tail(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(tail(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(tail(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(tail(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(tail(X)) -> tail#(proper(X)) ->
    tail#(mark(X)) -> tail#(X)
    proper#(tail(X)) -> tail#(proper(X)) -> tail#(ok(X)) -> tail#(X)
    proper#(head(X)) -> proper#(X) -> proper#(sieve(X)) -> proper#(X)
    proper#(head(X)) -> proper#(X) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(head(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(head(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(head(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(head(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(head(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(head(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(head(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(head(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X)
    proper#(head(X)) -> proper#(X) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(head(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X)
    proper#(head(X)) -> proper#(X) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(head(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(head(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(head(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(head(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(head(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(head(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(head(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(head(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(head(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(head(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(head(X)) -> head#(proper(X)) ->
    head#(mark(X)) -> head#(X)
    proper#(head(X)) -> head#(proper(X)) ->
    head#(ok(X)) -> head#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(head(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(tail(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X2) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(head(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(tail(X)) -> proper#(X)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> proper#(X1) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(sieve(X)) -> proper#(X)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(from(X)) -> proper#(X)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(sieve(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(s(X)) -> s#(proper(X))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(head(X)) -> proper#(X)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(tail(X)) -> proper#(X)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(sieve(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(sieve(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(sieve(X)) -> sieve#(proper(X)) ->
    sieve#(mark(X)) -> sieve#(X)
    proper#(sieve(X)) -> sieve#(proper(X)) ->
    sieve#(ok(X)) -> sieve#(X)
    proper#(from(X)) -> proper#(X) -> proper#(sieve(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(from(X)) -> from#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(head(X)) -> head#(proper(X))
    proper#(from(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X)
    proper#(from(X)) -> proper#(X) ->
    proper#(tail(X)) -> tail#(proper(X))
    proper#(from(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(from(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(from(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(from(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(from(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(from(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(from(X)) -> from#(proper(X)) ->
    from#(mark(X)) -> from#(X)
    proper#(from(X)) -> from#(proper(X)) -> from#(ok(X)) -> from#(X)
    proper#(s(X)) -> proper#(X) -> proper#(sieve(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) ->
    proper#(sieve(X)) -> sieve#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) ->
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(tail(X)) -> proper#(X)
    proper#(s(X)) -> proper#(X) -> proper#(tail(X)) -> tail#(proper(X))
    proper#(s(X)) -> proper#(X) -> proper#(if(X1,X2,X3)) -> proper#(X3)
    proper#(s(X)) -> proper#(X) -> proper#(if(X1,X2,X3)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) -> proper#(if(X1,X2,X3)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) ->
    proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
    proper#(s(X)) -> proper#(X) -> proper#(filter(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) -> proper#(filter(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) ->
    proper#(filter(X1,X2)) -> filter#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X2)
    proper#(s(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> proper#(X1)
    proper#(s(X)) -> proper#(X) ->
    proper#(divides(X1,X2)) -> divides#(proper(X1),proper(X2))
    proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
    proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
    tail#(ok(X)) -> tail#(X) -> tail#(mark(X)) -> tail#(X)
    tail#(ok(X)) -> tail#(X) -> tail#(ok(X)) -> tail#(X)
    tail#(mark(X)) -> tail#(X) -> tail#(mark(X)) -> tail#(X)
    tail#(mark(X)) -> tail#(X) -> tail#(ok(X)) -> tail#(X)
    head#(ok(X)) -> head#(X) -> head#(mark(X)) -> head#(X)
    head#(ok(X)) -> head#(X) -> head#(ok(X)) -> head#(X)
    head#(mark(X)) -> head#(X) -> head#(mark(X)) -> head#(X)
    head#(mark(X)) -> head#(X) ->
    head#(ok(X)) -> head#(X)
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3) ->
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2) ->
    divides#(mark(X1),X2) -> divides#(X1,X2)
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2) ->
    divides#(X1,mark(X2)) -> divides#(X1,X2)
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2) ->
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    divides#(mark(X1),X2) -> divides#(X1,X2) ->
    divides#(mark(X1),X2) -> divides#(X1,X2)
    divides#(mark(X1),X2) -> divides#(X1,X2) ->
    divides#(X1,mark(X2)) -> divides#(X1,X2)
    divides#(mark(X1),X2) -> divides#(X1,X2) ->
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    divides#(X1,mark(X2)) -> divides#(X1,X2) ->
    divides#(mark(X1),X2) -> divides#(X1,X2)
    divides#(X1,mark(X2)) -> divides#(X1,X2) ->
    divides#(X1,mark(X2)) -> divides#(X1,X2)
    divides#(X1,mark(X2)) -> divides#(X1,X2) ->
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2) ->
    filter#(mark(X1),X2) -> filter#(X1,X2)
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    filter#(mark(X1),X2) -> filter#(X1,X2) ->
    filter#(mark(X1),X2) -> filter#(X1,X2)
    filter#(mark(X1),X2) -> filter#(X1,X2) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    filter#(mark(X1),X2) -> filter#(X1,X2) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    filter#(X1,mark(X2)) -> filter#(X1,X2) ->
    filter#(mark(X1),X2) -> filter#(X1,X2)
    filter#(X1,mark(X2)) -> filter#(X1,X2) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    filter#(X1,mark(X2)) -> filter#(X1,X2) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    sieve#(ok(X)) -> sieve#(X) -> sieve#(mark(X)) -> sieve#(X)
    sieve#(ok(X)) -> sieve#(X) -> sieve#(ok(X)) -> sieve#(X)
    sieve#(mark(X)) -> sieve#(X) -> sieve#(mark(X)) -> sieve#(X)
    sieve#(mark(X)) -> sieve#(X) -> sieve#(ok(X)) -> sieve#(X)
    from#(ok(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
    from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
    from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X)
    from#(mark(X)) -> from#(X) -> from#(ok(X)) -> from#(X)
    s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
    s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
    s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
    active#(divides(X1,X2)) -> divides#(active(X1),X2) ->
    divides#(mark(X1),X2) -> divides#(X1,X2)
    active#(divides(X1,X2)) -> divides#(active(X1),X2) ->
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    active#(divides(X1,X2)) -> divides#(X1,active(X2)) ->
    divides#(X1,mark(X2)) -> divides#(X1,X2)
    active#(divides(X1,X2)) -> divides#(X1,active(X2)) ->
    divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(primes()) -> s#(0())
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(primes()) -> s#(s(0()))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(primes()) -> from#(s(s(0())))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> s#(X)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(s(X))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(sieve(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(active(X))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> s#(active(X))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(head(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(head(X)) -> head#(active(X))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(tail(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(tail(X)) -> tail#(active(X))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(divides(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(primes()) -> s#(0())
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(primes()) -> s#(s(0()))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(primes()) -> from#(s(s(0())))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(sieve(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(head(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(head(X)) -> head#(active(X))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(tail(X)) -> active#(X)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(tail(X)) -> tail#(active(X))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(divides(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) ->
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y)) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y))) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y) ->
    sieve#(ok(X)) -> sieve#(X)
    active#(filter(X1,X2)) -> filter#(active(X1),X2) ->
    filter#(mark(X1),X2) -> filter#(X1,X2)
    active#(filter(X1,X2)) -> filter#(active(X1),X2) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    active#(filter(X1,X2)) -> filter#(X1,active(X2)) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    active#(filter(X1,X2)) -> filter#(X1,active(X2)) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(primes()) -> s#(0())
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(primes()) -> s#(s(0()))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(primes()) -> from#(s(s(0())))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> s#(X)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(s(X))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(sieve(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(from(X)) -> from#(active(X))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(s(X)) -> s#(active(X))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(head(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(head(X)) -> head#(active(X))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(tail(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(tail(X)) -> tail#(active(X))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(filter(X1,X2)) -> active#(X2) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(primes()) -> s#(0())
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(primes()) -> s#(s(0()))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(primes()) -> from#(s(s(0())))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(sieve(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(head(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(head(X)) -> head#(active(X))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(tail(X)) -> active#(X)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(tail(X)) -> tail#(active(X))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(filter(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3) ->
    if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(primes()) -> s#(0())
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(primes()) -> s#(s(0()))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(primes()) -> from#(s(s(0())))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(sieve(X)) -> active#(X)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(head(X)) -> active#(X)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(head(X)) -> head#(active(X))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(tail(X)) -> active#(X)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(tail(X)) -> tail#(active(X))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(if(X1,X2,X3)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(tail(X)) -> tail#(active(X)) ->
    tail#(mark(X)) -> tail#(X)
    active#(tail(X)) -> tail#(active(X)) -> tail#(ok(X)) -> tail#(X)
    active#(tail(X)) -> active#(X) -> active#(primes()) -> s#(0())
    active#(tail(X)) -> active#(X) -> active#(primes()) -> s#(s(0()))
    active#(tail(X)) -> active#(X) ->
    active#(primes()) -> from#(s(s(0())))
    active#(tail(X)) -> active#(X) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(tail(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(tail(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(tail(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(tail(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(tail(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(tail(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(tail(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(tail(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(tail(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(tail(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(tail(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(tail(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(tail(X)) -> active#(X) -> active#(sieve(X)) -> active#(X)
    active#(tail(X)) -> active#(X) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(tail(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(tail(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(tail(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(tail(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(tail(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(tail(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(tail(X)) -> active#(X) -> active#(head(X)) -> active#(X)
    active#(tail(X)) -> active#(X) ->
    active#(head(X)) -> head#(active(X))
    active#(tail(X)) -> active#(X) -> active#(tail(X)) -> active#(X)
    active#(tail(X)) -> active#(X) ->
    active#(tail(X)) -> tail#(active(X))
    active#(tail(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(tail(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(tail(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(tail(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(tail(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(tail(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(tail(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(tail(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(tail(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(tail(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(head(X)) -> head#(active(X)) ->
    head#(mark(X)) -> head#(X)
    active#(head(X)) -> head#(active(X)) -> head#(ok(X)) -> head#(X)
    active#(head(X)) -> active#(X) -> active#(primes()) -> s#(0())
    active#(head(X)) -> active#(X) -> active#(primes()) -> s#(s(0()))
    active#(head(X)) -> active#(X) ->
    active#(primes()) -> from#(s(s(0())))
    active#(head(X)) -> active#(X) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(head(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(head(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(head(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(head(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(head(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(head(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(head(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(head(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(head(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(head(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(head(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(head(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(head(X)) -> active#(X) -> active#(sieve(X)) -> active#(X)
    active#(head(X)) -> active#(X) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(head(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(head(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(head(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(head(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(head(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(head(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(head(X)) -> active#(X) -> active#(head(X)) -> active#(X)
    active#(head(X)) -> active#(X) ->
    active#(head(X)) -> head#(active(X))
    active#(head(X)) -> active#(X) -> active#(tail(X)) -> active#(X)
    active#(head(X)) -> active#(X) ->
    active#(tail(X)) -> tail#(active(X))
    active#(head(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(head(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(head(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(head(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(head(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(head(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(head(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(head(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(head(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(head(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
    cons#(mark(X1),X2) -> cons#(X1,X2)
    active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(primes()) -> s#(0())
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(primes()) -> s#(s(0()))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(primes()) -> from#(s(s(0())))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> s#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(s(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sieve(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(from(X)) -> from#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(s(X)) -> s#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(head(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(head(X)) -> head#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(tail(X)) -> active#(X)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(tail(X)) -> tail#(active(X))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(cons(X1,X2)) -> active#(X1) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y)) ->
    filter#(X1,mark(X2)) -> filter#(X1,X2)
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y)) ->
    filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y))) ->
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    active#(sieve(cons(X,Y))) -> sieve#(Y) ->
    sieve#(mark(X)) -> sieve#(X)
    active#(sieve(cons(X,Y))) -> sieve#(Y) ->
    sieve#(ok(X)) -> sieve#(X)
    active#(sieve(X)) -> sieve#(active(X)) ->
    sieve#(mark(X)) -> sieve#(X)
    active#(sieve(X)) -> sieve#(active(X)) ->
    sieve#(ok(X)) -> sieve#(X)
    active#(sieve(X)) -> active#(X) -> active#(primes()) -> s#(0())
    active#(sieve(X)) -> active#(X) ->
    active#(primes()) -> s#(s(0()))
    active#(sieve(X)) -> active#(X) ->
    active#(primes()) -> from#(s(s(0())))
    active#(sieve(X)) -> active#(X) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(sieve(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(sieve(X)) -> active#(X) ->
    active#(from(X)) -> from#(s(X))
    active#(sieve(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(sieve(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(sieve(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(sieve(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(sieve(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(sieve(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(sieve(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(sieve(X)) -> active#(X) ->
    active#(sieve(X)) -> active#(X)
    active#(sieve(X)) -> active#(X) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(sieve(X)) -> active#(X) ->
    active#(from(X)) -> active#(X)
    active#(sieve(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(sieve(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(sieve(X)) -> active#(X) ->
    active#(s(X)) -> s#(active(X))
    active#(sieve(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(sieve(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(sieve(X)) -> active#(X) ->
    active#(head(X)) -> active#(X)
    active#(sieve(X)) -> active#(X) ->
    active#(head(X)) -> head#(active(X))
    active#(sieve(X)) -> active#(X) ->
    active#(tail(X)) -> active#(X)
    active#(sieve(X)) -> active#(X) ->
    active#(tail(X)) -> tail#(active(X))
    active#(sieve(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(sieve(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(sieve(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(sieve(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(sieve(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(sieve(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(sieve(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(from(X)) -> from#(active(X)) ->
    from#(mark(X)) -> from#(X)
    active#(from(X)) -> from#(active(X)) -> from#(ok(X)) -> from#(X)
    active#(from(X)) -> active#(X) -> active#(primes()) -> s#(0())
    active#(from(X)) -> active#(X) -> active#(primes()) -> s#(s(0()))
    active#(from(X)) -> active#(X) ->
    active#(primes()) -> from#(s(s(0())))
    active#(from(X)) -> active#(X) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(from(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(from(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(from(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(from(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(from(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(from(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(from(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(from(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(from(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(from(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(from(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(from(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(from(X)) -> active#(X) -> active#(sieve(X)) -> active#(X)
    active#(from(X)) -> active#(X) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(from(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(from(X)) -> active#(X) ->
    active#(from(X)) -> from#(active(X))
    active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(from(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(from(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(from(X)) -> active#(X) -> active#(head(X)) -> active#(X)
    active#(from(X)) -> active#(X) ->
    active#(head(X)) -> head#(active(X))
    active#(from(X)) -> active#(X) -> active#(tail(X)) -> active#(X)
    active#(from(X)) -> active#(X) ->
    active#(tail(X)) -> tail#(active(X))
    active#(from(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(from(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> active#(X2)
    active#(from(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(from(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(from(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(from(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(from(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(X1,active(X2))
    active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
    active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
    active#(s(X)) -> active#(X) -> active#(primes()) -> s#(0())
    active#(s(X)) -> active#(X) -> active#(primes()) -> s#(s(0()))
    active#(s(X)) -> active#(X) -> active#(primes()) -> from#(s(s(0())))
    active#(s(X)) -> active#(X) ->
    active#(primes()) -> sieve#(from(s(s(0()))))
    active#(s(X)) -> active#(X) -> active#(from(X)) -> s#(X)
    active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(s(X))
    active#(s(X)) -> active#(X) ->
    active#(from(X)) -> cons#(X,from(s(X)))
    active#(s(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> sieve#(Y)
    active#(s(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(X,sieve(Y))
    active#(s(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> cons#(Y,filter(X,sieve(Y)))
    active#(s(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> filter#(s(s(X)),Z)
    active#(s(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) -> divides#(s(s(X)),Y)
    active#(s(X)) -> active#(X) ->
    active#(filter(s(s(X)),cons(Y,Z))) ->
    if#(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
    active#(s(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> sieve#(Y)
    active#(s(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> filter#(X,sieve(Y))
    active#(s(X)) -> active#(X) ->
    active#(sieve(cons(X,Y))) -> cons#(X,filter(X,sieve(Y)))
    active#(s(X)) -> active#(X) -> active#(sieve(X)) -> active#(X)
    active#(s(X)) -> active#(X) ->
    active#(sieve(X)) -> sieve#(active(X))
    active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X)
    active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(active(X))
    active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
    active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
    active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) ->
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(head(X)) -> active#(X)
    active#(s(X)) -> active#(X) -> active#(head(X)) -> head#(active(X))
    active#(s(X)) -> active#(X) -> active#(tail(X)) -> active#(X)
    active#(s(X)) -> active#(X) -> active#(tail(X)) -> tail#(active(X))
    active#(s(X)) -> active#(X) -> active#(if(X1,X2,X3)) -> active#(X1)
    active#(s(X)) -> active#(X) ->
    active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
    active#(s(X)) -> active#(X) -> active#(filter(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(active(X1),X2)
    active#(s(X)) -> active#(X) -> active#(filter(X1,X2)) -> active#(X2)
    active#(s(X)) -> active#(X) ->
    active#(filter(X1,X2)) -> filter#(X1,active(X2))
    active#(s(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X1)
    active#(s(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> divides#(active(X1),X2)
    active#(s(X)) -> active#(X) ->
    active#(divides(X1,X2)) -> active#(X2)
    active#(s(X)) -> active#(X) -> active#(divides(X1,X2)) -> divides#(X1,active(X2))
   SCC Processor:
    #sccs: 12
    #rules: 47
    #arcs: 908/7225
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X))
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     proper#(divides(X1,X2)) -> proper#(X1)
     proper#(divides(X1,X2)) -> proper#(X2)
     proper#(filter(X1,X2)) -> proper#(X1)
     proper#(filter(X1,X2)) -> proper#(X2)
     proper#(if(X1,X2,X3)) -> proper#(X1)
     proper#(if(X1,X2,X3)) -> proper#(X2)
     proper#(if(X1,X2,X3)) -> proper#(X3)
     proper#(tail(X)) -> proper#(X)
     proper#(head(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(s(X)) -> proper#(X)
     proper#(from(X)) -> proper#(X)
     proper#(sieve(X)) -> proper#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [proper#](x0) = x0 + 1,
      
      [top](x0) = 1,
      
      [ok](x0) = x0,
      
      [proper](x0) = x0,
      
      [divides](x0, x1) = x0 + x1 + 1,
      
      [filter](x0, x1) = x0 + x1 + 1,
      
      [false] = 1,
      
      [if](x0, x1, x2) = x0 + x1 + x2,
      
      [true] = 1,
      
      [tail](x0) = x0,
      
      [head](x0) = x0,
      
      [cons](x0, x1) = x0 + x1,
      
      [mark](x0) = 1,
      
      [sieve](x0) = x0,
      
      [from](x0) = x0 + 1,
      
      [s](x0) = x0,
      
      [0] = 0,
      
      [active](x0) = x0 + 1,
      
      [primes] = 0
     orientation:
      proper#(divides(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1)
      
      proper#(divides(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2)
      
      proper#(filter(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1)
      
      proper#(filter(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2)
      
      proper#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = proper#(X1)
      
      proper#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X2 + 1 = proper#(X2)
      
      proper#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X3 + 1 = proper#(X3)
      
      proper#(tail(X)) = X + 1 >= X + 1 = proper#(X)
      
      proper#(head(X)) = X + 1 >= X + 1 = proper#(X)
      
      proper#(cons(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1)
      
      proper#(cons(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2)
      
      proper#(s(X)) = X + 1 >= X + 1 = proper#(X)
      
      proper#(from(X)) = X + 2 >= X + 1 = proper#(X)
      
      proper#(sieve(X)) = X + 1 >= X + 1 = proper#(X)
      
      active(primes()) = 1 >= 1 = mark(sieve(from(s(s(0())))))
      
      active(from(X)) = X + 2 >= 1 = mark(cons(X,from(s(X))))
      
      active(head(cons(X,Y))) = X + Y + 1 >= 1 = mark(X)
      
      active(tail(cons(X,Y))) = X + Y + 1 >= 1 = mark(Y)
      
      active(if(true(),X,Y)) = X + Y + 2 >= 1 = mark(X)
      
      active(if(false(),X,Y)) = X + Y + 2 >= 1 = mark(Y)
      
      active(filter(s(s(X)),cons(Y,Z))) = X + Y + Z + 2 >= 1 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
      
      active(sieve(cons(X,Y))) = X + Y + 1 >= 1 = mark(cons(X,filter(X,sieve(Y))))
      
      active(sieve(X)) = X + 1 >= X + 1 = sieve(active(X))
      
      active(from(X)) = X + 2 >= X + 2 = from(active(X))
      
      active(s(X)) = X + 1 >= X + 1 = s(active(X))
      
      active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2)
      
      active(head(X)) = X + 1 >= X + 1 = head(active(X))
      
      active(tail(X)) = X + 1 >= X + 1 = tail(active(X))
      
      active(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = if(active(X1),X2,X3)
      
      active(filter(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = filter(active(X1),X2)
      
      active(filter(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = filter(X1,active(X2))
      
      active(divides(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = divides(active(X1),X2)
      
      active(divides(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = divides(X1,active(X2))
      
      sieve(mark(X)) = 1 >= 1 = mark(sieve(X))
      
      from(mark(X)) = 2 >= 1 = mark(from(X))
      
      s(mark(X)) = 1 >= 1 = mark(s(X))
      
      cons(mark(X1),X2) = X2 + 1 >= 1 = mark(cons(X1,X2))
      
      head(mark(X)) = 1 >= 1 = mark(head(X))
      
      tail(mark(X)) = 1 >= 1 = mark(tail(X))
      
      if(mark(X1),X2,X3) = X2 + X3 + 1 >= 1 = mark(if(X1,X2,X3))
      
      filter(mark(X1),X2) = X2 + 2 >= 1 = mark(filter(X1,X2))
      
      filter(X1,mark(X2)) = X1 + 2 >= 1 = mark(filter(X1,X2))
      
      divides(mark(X1),X2) = X2 + 2 >= 1 = mark(divides(X1,X2))
      
      divides(X1,mark(X2)) = X1 + 2 >= 1 = mark(divides(X1,X2))
      
      proper(primes()) = 0 >= 0 = ok(primes())
      
      proper(sieve(X)) = X >= X = sieve(proper(X))
      
      proper(from(X)) = X + 1 >= X + 1 = from(proper(X))
      
      proper(s(X)) = X >= X = s(proper(X))
      
      proper(0()) = 0 >= 0 = ok(0())
      
      proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2))
      
      proper(head(X)) = X >= X = head(proper(X))
      
      proper(tail(X)) = X >= X = tail(proper(X))
      
      proper(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = if(proper(X1),proper(X2),proper(X3))
      
      proper(true()) = 1 >= 1 = ok(true())
      
      proper(false()) = 1 >= 1 = ok(false())
      
      proper(filter(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = filter(proper(X1),proper(X2))
      
      proper(divides(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = divides(proper(X1),proper(X2))
      
      sieve(ok(X)) = X >= X = ok(sieve(X))
      
      from(ok(X)) = X + 1 >= X + 1 = ok(from(X))
      
      s(ok(X)) = X >= X = ok(s(X))
      
      cons(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(cons(X1,X2))
      
      head(ok(X)) = X >= X = ok(head(X))
      
      tail(ok(X)) = X >= X = ok(tail(X))
      
      if(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(if(X1,X2,X3))
      
      filter(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(filter(X1,X2))
      
      divides(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(divides(X1,X2))
      
      top(mark(X)) = 1 >= 1 = top(proper(X))
      
      top(ok(X)) = 1 >= 1 = top(active(X))
     problem:
      DPs:
       proper#(if(X1,X2,X3)) -> proper#(X1)
       proper#(if(X1,X2,X3)) -> proper#(X2)
       proper#(if(X1,X2,X3)) -> proper#(X3)
       proper#(tail(X)) -> proper#(X)
       proper#(head(X)) -> proper#(X)
       proper#(cons(X1,X2)) -> proper#(X1)
       proper#(cons(X1,X2)) -> proper#(X2)
       proper#(s(X)) -> proper#(X)
       proper#(sieve(X)) -> proper#(X)
      TRS:
       active(primes()) -> mark(sieve(from(s(s(0())))))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(head(cons(X,Y))) -> mark(X)
       active(tail(cons(X,Y))) -> mark(Y)
       active(if(true(),X,Y)) -> mark(X)
       active(if(false(),X,Y)) -> mark(Y)
       active(filter(s(s(X)),cons(Y,Z))) ->
       mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
       active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
       active(sieve(X)) -> sieve(active(X))
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(head(X)) -> head(active(X))
       active(tail(X)) -> tail(active(X))
       active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
       active(filter(X1,X2)) -> filter(active(X1),X2)
       active(filter(X1,X2)) -> filter(X1,active(X2))
       active(divides(X1,X2)) -> divides(active(X1),X2)
       active(divides(X1,X2)) -> divides(X1,active(X2))
       sieve(mark(X)) -> mark(sieve(X))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       head(mark(X)) -> mark(head(X))
       tail(mark(X)) -> mark(tail(X))
       if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
       filter(mark(X1),X2) -> mark(filter(X1,X2))
       filter(X1,mark(X2)) -> mark(filter(X1,X2))
       divides(mark(X1),X2) -> mark(divides(X1,X2))
       divides(X1,mark(X2)) -> mark(divides(X1,X2))
       proper(primes()) -> ok(primes())
       proper(sieve(X)) -> sieve(proper(X))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(0()) -> ok(0())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(head(X)) -> head(proper(X))
       proper(tail(X)) -> tail(proper(X))
       proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
       proper(true()) -> ok(true())
       proper(false()) -> ok(false())
       proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
       proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
       sieve(ok(X)) -> ok(sieve(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       head(ok(X)) -> ok(head(X))
       tail(ok(X)) -> ok(tail(X))
       if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
       filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
       divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [proper#](x0) = x0,
       
       [top](x0) = 0,
       
       [ok](x0) = x0,
       
       [proper](x0) = x0,
       
       [divides](x0, x1) = 1,
       
       [filter](x0, x1) = 1,
       
       [false] = 0,
       
       [if](x0, x1, x2) = x0 + x1 + x2,
       
       [true] = 0,
       
       [tail](x0) = x0,
       
       [head](x0) = x0,
       
       [cons](x0, x1) = x0 + x1,
       
       [mark](x0) = 1,
       
       [sieve](x0) = x0 + 1,
       
       [from](x0) = x0 + 1,
       
       [s](x0) = x0,
       
       [0] = 0,
       
       [active](x0) = x0 + 1,
       
       [primes] = 0
      orientation:
       proper#(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 = proper#(X1)
       
       proper#(if(X1,X2,X3)) = X1 + X2 + X3 >= X2 = proper#(X2)
       
       proper#(if(X1,X2,X3)) = X1 + X2 + X3 >= X3 = proper#(X3)
       
       proper#(tail(X)) = X >= X = proper#(X)
       
       proper#(head(X)) = X >= X = proper#(X)
       
       proper#(cons(X1,X2)) = X1 + X2 >= X1 = proper#(X1)
       
       proper#(cons(X1,X2)) = X1 + X2 >= X2 = proper#(X2)
       
       proper#(s(X)) = X >= X = proper#(X)
       
       proper#(sieve(X)) = X + 1 >= X = proper#(X)
       
       active(primes()) = 1 >= 1 = mark(sieve(from(s(s(0())))))
       
       active(from(X)) = X + 2 >= 1 = mark(cons(X,from(s(X))))
       
       active(head(cons(X,Y))) = X + Y + 1 >= 1 = mark(X)
       
       active(tail(cons(X,Y))) = X + Y + 1 >= 1 = mark(Y)
       
       active(if(true(),X,Y)) = X + Y + 1 >= 1 = mark(X)
       
       active(if(false(),X,Y)) = X + Y + 1 >= 1 = mark(Y)
       
       active(filter(s(s(X)),cons(Y,Z))) = 2 >= 1 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
       
       active(sieve(cons(X,Y))) = X + Y + 2 >= 1 = mark(cons(X,filter(X,sieve(Y))))
       
       active(sieve(X)) = X + 2 >= X + 2 = sieve(active(X))
       
       active(from(X)) = X + 2 >= X + 2 = from(active(X))
       
       active(s(X)) = X + 1 >= X + 1 = s(active(X))
       
       active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2)
       
       active(head(X)) = X + 1 >= X + 1 = head(active(X))
       
       active(tail(X)) = X + 1 >= X + 1 = tail(active(X))
       
       active(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = if(active(X1),X2,X3)
       
       active(filter(X1,X2)) = 2 >= 1 = filter(active(X1),X2)
       
       active(filter(X1,X2)) = 2 >= 1 = filter(X1,active(X2))
       
       active(divides(X1,X2)) = 2 >= 1 = divides(active(X1),X2)
       
       active(divides(X1,X2)) = 2 >= 1 = divides(X1,active(X2))
       
       sieve(mark(X)) = 2 >= 1 = mark(sieve(X))
       
       from(mark(X)) = 2 >= 1 = mark(from(X))
       
       s(mark(X)) = 1 >= 1 = mark(s(X))
       
       cons(mark(X1),X2) = X2 + 1 >= 1 = mark(cons(X1,X2))
       
       head(mark(X)) = 1 >= 1 = mark(head(X))
       
       tail(mark(X)) = 1 >= 1 = mark(tail(X))
       
       if(mark(X1),X2,X3) = X2 + X3 + 1 >= 1 = mark(if(X1,X2,X3))
       
       filter(mark(X1),X2) = 1 >= 1 = mark(filter(X1,X2))
       
       filter(X1,mark(X2)) = 1 >= 1 = mark(filter(X1,X2))
       
       divides(mark(X1),X2) = 1 >= 1 = mark(divides(X1,X2))
       
       divides(X1,mark(X2)) = 1 >= 1 = mark(divides(X1,X2))
       
       proper(primes()) = 0 >= 0 = ok(primes())
       
       proper(sieve(X)) = X + 1 >= X + 1 = sieve(proper(X))
       
       proper(from(X)) = X + 1 >= X + 1 = from(proper(X))
       
       proper(s(X)) = X >= X = s(proper(X))
       
       proper(0()) = 0 >= 0 = ok(0())
       
       proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2))
       
       proper(head(X)) = X >= X = head(proper(X))
       
       proper(tail(X)) = X >= X = tail(proper(X))
       
       proper(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = if(proper(X1),proper(X2),proper(X3))
       
       proper(true()) = 0 >= 0 = ok(true())
       
       proper(false()) = 0 >= 0 = ok(false())
       
       proper(filter(X1,X2)) = 1 >= 1 = filter(proper(X1),proper(X2))
       
       proper(divides(X1,X2)) = 1 >= 1 = divides(proper(X1),proper(X2))
       
       sieve(ok(X)) = X + 1 >= X + 1 = ok(sieve(X))
       
       from(ok(X)) = X + 1 >= X + 1 = ok(from(X))
       
       s(ok(X)) = X >= X = ok(s(X))
       
       cons(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(cons(X1,X2))
       
       head(ok(X)) = X >= X = ok(head(X))
       
       tail(ok(X)) = X >= X = ok(tail(X))
       
       if(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = ok(if(X1,X2,X3))
       
       filter(ok(X1),ok(X2)) = 1 >= 1 = ok(filter(X1,X2))
       
       divides(ok(X1),ok(X2)) = 1 >= 1 = ok(divides(X1,X2))
       
       top(mark(X)) = 0 >= 0 = top(proper(X))
       
       top(ok(X)) = 0 >= 0 = top(active(X))
      problem:
       DPs:
        proper#(if(X1,X2,X3)) -> proper#(X1)
        proper#(if(X1,X2,X3)) -> proper#(X2)
        proper#(if(X1,X2,X3)) -> proper#(X3)
        proper#(tail(X)) -> proper#(X)
        proper#(head(X)) -> proper#(X)
        proper#(cons(X1,X2)) -> proper#(X1)
        proper#(cons(X1,X2)) -> proper#(X2)
        proper#(s(X)) -> proper#(X)
       TRS:
        active(primes()) -> mark(sieve(from(s(s(0())))))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(head(cons(X,Y))) -> mark(X)
        active(tail(cons(X,Y))) -> mark(Y)
        active(if(true(),X,Y)) -> mark(X)
        active(if(false(),X,Y)) -> mark(Y)
        active(filter(s(s(X)),cons(Y,Z))) ->
        mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
        active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
        active(sieve(X)) -> sieve(active(X))
        active(from(X)) -> from(active(X))
        active(s(X)) -> s(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(head(X)) -> head(active(X))
        active(tail(X)) -> tail(active(X))
        active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
        active(filter(X1,X2)) -> filter(active(X1),X2)
        active(filter(X1,X2)) -> filter(X1,active(X2))
        active(divides(X1,X2)) -> divides(active(X1),X2)
        active(divides(X1,X2)) -> divides(X1,active(X2))
        sieve(mark(X)) -> mark(sieve(X))
        from(mark(X)) -> mark(from(X))
        s(mark(X)) -> mark(s(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        head(mark(X)) -> mark(head(X))
        tail(mark(X)) -> mark(tail(X))
        if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
        filter(mark(X1),X2) -> mark(filter(X1,X2))
        filter(X1,mark(X2)) -> mark(filter(X1,X2))
        divides(mark(X1),X2) -> mark(divides(X1,X2))
        divides(X1,mark(X2)) -> mark(divides(X1,X2))
        proper(primes()) -> ok(primes())
        proper(sieve(X)) -> sieve(proper(X))
        proper(from(X)) -> from(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(head(X)) -> head(proper(X))
        proper(tail(X)) -> tail(proper(X))
        proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
        proper(true()) -> ok(true())
        proper(false()) -> ok(false())
        proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
        proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
        sieve(ok(X)) -> ok(sieve(X))
        from(ok(X)) -> ok(from(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        head(ok(X)) -> ok(head(X))
        tail(ok(X)) -> ok(tail(X))
        if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
        filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
        divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [proper#](x0) = x0 + 1,
        
        [top](x0) = 0,
        
        [ok](x0) = x0,
        
        [proper](x0) = x0,
        
        [divides](x0, x1) = 0,
        
        [filter](x0, x1) = x1,
        
        [false] = 0,
        
        [if](x0, x1, x2) = x0 + x1 + x2 + 1,
        
        [true] = 0,
        
        [tail](x0) = x0 + 1,
        
        [head](x0) = x0 + 1,
        
        [cons](x0, x1) = x0 + x1 + 1,
        
        [mark](x0) = 0,
        
        [sieve](x0) = 1,
        
        [from](x0) = 0,
        
        [s](x0) = x0 + 1,
        
        [0] = 0,
        
        [active](x0) = x0,
        
        [primes] = 0
       orientation:
        proper#(if(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X1 + 1 = proper#(X1)
        
        proper#(if(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X2 + 1 = proper#(X2)
        
        proper#(if(X1,X2,X3)) = X1 + X2 + X3 + 2 >= X3 + 1 = proper#(X3)
        
        proper#(tail(X)) = X + 2 >= X + 1 = proper#(X)
        
        proper#(head(X)) = X + 2 >= X + 1 = proper#(X)
        
        proper#(cons(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1)
        
        proper#(cons(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2)
        
        proper#(s(X)) = X + 2 >= X + 1 = proper#(X)
        
        active(primes()) = 0 >= 0 = mark(sieve(from(s(s(0())))))
        
        active(from(X)) = 0 >= 0 = mark(cons(X,from(s(X))))
        
        active(head(cons(X,Y))) = X + Y + 2 >= 0 = mark(X)
        
        active(tail(cons(X,Y))) = X + Y + 2 >= 0 = mark(Y)
        
        active(if(true(),X,Y)) = X + Y + 1 >= 0 = mark(X)
        
        active(if(false(),X,Y)) = X + Y + 1 >= 0 = mark(Y)
        
        active(filter(s(s(X)),cons(Y,Z))) = Y + Z + 1 >= 0 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
        
        active(sieve(cons(X,Y))) = 1 >= 0 = mark(cons(X,filter(X,sieve(Y))))
        
        active(sieve(X)) = 1 >= 1 = sieve(active(X))
        
        active(from(X)) = 0 >= 0 = from(active(X))
        
        active(s(X)) = X + 1 >= X + 1 = s(active(X))
        
        active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2)
        
        active(head(X)) = X + 1 >= X + 1 = head(active(X))
        
        active(tail(X)) = X + 1 >= X + 1 = tail(active(X))
        
        active(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = if(active(X1),X2,X3)
        
        active(filter(X1,X2)) = X2 >= X2 = filter(active(X1),X2)
        
        active(filter(X1,X2)) = X2 >= X2 = filter(X1,active(X2))
        
        active(divides(X1,X2)) = 0 >= 0 = divides(active(X1),X2)
        
        active(divides(X1,X2)) = 0 >= 0 = divides(X1,active(X2))
        
        sieve(mark(X)) = 1 >= 0 = mark(sieve(X))
        
        from(mark(X)) = 0 >= 0 = mark(from(X))
        
        s(mark(X)) = 1 >= 0 = mark(s(X))
        
        cons(mark(X1),X2) = X2 + 1 >= 0 = mark(cons(X1,X2))
        
        head(mark(X)) = 1 >= 0 = mark(head(X))
        
        tail(mark(X)) = 1 >= 0 = mark(tail(X))
        
        if(mark(X1),X2,X3) = X2 + X3 + 1 >= 0 = mark(if(X1,X2,X3))
        
        filter(mark(X1),X2) = X2 >= 0 = mark(filter(X1,X2))
        
        filter(X1,mark(X2)) = 0 >= 0 = mark(filter(X1,X2))
        
        divides(mark(X1),X2) = 0 >= 0 = mark(divides(X1,X2))
        
        divides(X1,mark(X2)) = 0 >= 0 = mark(divides(X1,X2))
        
        proper(primes()) = 0 >= 0 = ok(primes())
        
        proper(sieve(X)) = 1 >= 1 = sieve(proper(X))
        
        proper(from(X)) = 0 >= 0 = from(proper(X))
        
        proper(s(X)) = X + 1 >= X + 1 = s(proper(X))
        
        proper(0()) = 0 >= 0 = ok(0())
        
        proper(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(proper(X1),proper(X2))
        
        proper(head(X)) = X + 1 >= X + 1 = head(proper(X))
        
        proper(tail(X)) = X + 1 >= X + 1 = tail(proper(X))
        
        proper(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = if(proper(X1),proper(X2),proper(X3))
        
        proper(true()) = 0 >= 0 = ok(true())
        
        proper(false()) = 0 >= 0 = ok(false())
        
        proper(filter(X1,X2)) = X2 >= X2 = filter(proper(X1),proper(X2))
        
        proper(divides(X1,X2)) = 0 >= 0 = divides(proper(X1),proper(X2))
        
        sieve(ok(X)) = 1 >= 1 = ok(sieve(X))
        
        from(ok(X)) = 0 >= 0 = ok(from(X))
        
        s(ok(X)) = X + 1 >= X + 1 = ok(s(X))
        
        cons(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(cons(X1,X2))
        
        head(ok(X)) = X + 1 >= X + 1 = ok(head(X))
        
        tail(ok(X)) = X + 1 >= X + 1 = ok(tail(X))
        
        if(ok(X1),ok(X2),ok(X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = ok(if(X1,X2,X3))
        
        filter(ok(X1),ok(X2)) = X2 >= X2 = ok(filter(X1,X2))
        
        divides(ok(X1),ok(X2)) = 0 >= 0 = ok(divides(X1,X2))
        
        top(mark(X)) = 0 >= 0 = top(proper(X))
        
        top(ok(X)) = 0 >= 0 = top(active(X))
       problem:
        DPs:
         
        TRS:
         active(primes()) -> mark(sieve(from(s(s(0())))))
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(head(cons(X,Y))) -> mark(X)
         active(tail(cons(X,Y))) -> mark(Y)
         active(if(true(),X,Y)) -> mark(X)
         active(if(false(),X,Y)) -> mark(Y)
         active(filter(s(s(X)),cons(Y,Z))) ->
         mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
         active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
         active(sieve(X)) -> sieve(active(X))
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(head(X)) -> head(active(X))
         active(tail(X)) -> tail(active(X))
         active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
         active(filter(X1,X2)) -> filter(active(X1),X2)
         active(filter(X1,X2)) -> filter(X1,active(X2))
         active(divides(X1,X2)) -> divides(active(X1),X2)
         active(divides(X1,X2)) -> divides(X1,active(X2))
         sieve(mark(X)) -> mark(sieve(X))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         head(mark(X)) -> mark(head(X))
         tail(mark(X)) -> mark(tail(X))
         if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
         filter(mark(X1),X2) -> mark(filter(X1,X2))
         filter(X1,mark(X2)) -> mark(filter(X1,X2))
         divides(mark(X1),X2) -> mark(divides(X1,X2))
         divides(X1,mark(X2)) -> mark(divides(X1,X2))
         proper(primes()) -> ok(primes())
         proper(sieve(X)) -> sieve(proper(X))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         proper(0()) -> ok(0())
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(head(X)) -> head(proper(X))
         proper(tail(X)) -> tail(proper(X))
         proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
         proper(true()) -> ok(true())
         proper(false()) -> ok(false())
         proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
         proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
         sieve(ok(X)) -> ok(sieve(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
         head(ok(X)) -> ok(head(X))
         tail(ok(X)) -> ok(tail(X))
         if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
         filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
         divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
    
    DPs:
     active#(divides(X1,X2)) -> active#(X2)
     active#(divides(X1,X2)) -> active#(X1)
     active#(filter(X1,X2)) -> active#(X2)
     active#(filter(X1,X2)) -> active#(X1)
     active#(if(X1,X2,X3)) -> active#(X1)
     active#(tail(X)) -> active#(X)
     active#(head(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1)
     active#(s(X)) -> active#(X)
     active#(from(X)) -> active#(X)
     active#(sieve(X)) -> active#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [active#](x0) = x0 + 1,
      
      [top](x0) = 0,
      
      [ok](x0) = 0,
      
      [proper](x0) = x0,
      
      [divides](x0, x1) = x0 + x1 + 1,
      
      [filter](x0, x1) = x0 + x1 + 1,
      
      [false] = 0,
      
      [if](x0, x1, x2) = x0 + 1,
      
      [true] = 0,
      
      [tail](x0) = x0 + 1,
      
      [head](x0) = x0 + 1,
      
      [cons](x0, x1) = x0 + x1 + 1,
      
      [mark](x0) = 1,
      
      [sieve](x0) = x0,
      
      [from](x0) = x0 + 1,
      
      [s](x0) = x0,
      
      [0] = 0,
      
      [active](x0) = x0,
      
      [primes] = 1
     orientation:
      active#(divides(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2)
      
      active#(divides(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1)
      
      active#(filter(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2)
      
      active#(filter(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1)
      
      active#(if(X1,X2,X3)) = X1 + 2 >= X1 + 1 = active#(X1)
      
      active#(tail(X)) = X + 2 >= X + 1 = active#(X)
      
      active#(head(X)) = X + 2 >= X + 1 = active#(X)
      
      active#(cons(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1)
      
      active#(s(X)) = X + 1 >= X + 1 = active#(X)
      
      active#(from(X)) = X + 2 >= X + 1 = active#(X)
      
      active#(sieve(X)) = X + 1 >= X + 1 = active#(X)
      
      active(primes()) = 1 >= 1 = mark(sieve(from(s(s(0())))))
      
      active(from(X)) = X + 1 >= 1 = mark(cons(X,from(s(X))))
      
      active(head(cons(X,Y))) = X + Y + 2 >= 1 = mark(X)
      
      active(tail(cons(X,Y))) = X + Y + 2 >= 1 = mark(Y)
      
      active(if(true(),X,Y)) = 1 >= 1 = mark(X)
      
      active(if(false(),X,Y)) = 1 >= 1 = mark(Y)
      
      active(filter(s(s(X)),cons(Y,Z))) = X + Y + Z + 2 >= 1 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
      
      active(sieve(cons(X,Y))) = X + Y + 1 >= 1 = mark(cons(X,filter(X,sieve(Y))))
      
      active(sieve(X)) = X >= X = sieve(active(X))
      
      active(from(X)) = X + 1 >= X + 1 = from(active(X))
      
      active(s(X)) = X >= X = s(active(X))
      
      active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2)
      
      active(head(X)) = X + 1 >= X + 1 = head(active(X))
      
      active(tail(X)) = X + 1 >= X + 1 = tail(active(X))
      
      active(if(X1,X2,X3)) = X1 + 1 >= X1 + 1 = if(active(X1),X2,X3)
      
      active(filter(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = filter(active(X1),X2)
      
      active(filter(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = filter(X1,active(X2))
      
      active(divides(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = divides(active(X1),X2)
      
      active(divides(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = divides(X1,active(X2))
      
      sieve(mark(X)) = 1 >= 1 = mark(sieve(X))
      
      from(mark(X)) = 2 >= 1 = mark(from(X))
      
      s(mark(X)) = 1 >= 1 = mark(s(X))
      
      cons(mark(X1),X2) = X2 + 2 >= 1 = mark(cons(X1,X2))
      
      head(mark(X)) = 2 >= 1 = mark(head(X))
      
      tail(mark(X)) = 2 >= 1 = mark(tail(X))
      
      if(mark(X1),X2,X3) = 2 >= 1 = mark(if(X1,X2,X3))
      
      filter(mark(X1),X2) = X2 + 2 >= 1 = mark(filter(X1,X2))
      
      filter(X1,mark(X2)) = X1 + 2 >= 1 = mark(filter(X1,X2))
      
      divides(mark(X1),X2) = X2 + 2 >= 1 = mark(divides(X1,X2))
      
      divides(X1,mark(X2)) = X1 + 2 >= 1 = mark(divides(X1,X2))
      
      proper(primes()) = 1 >= 0 = ok(primes())
      
      proper(sieve(X)) = X >= X = sieve(proper(X))
      
      proper(from(X)) = X + 1 >= X + 1 = from(proper(X))
      
      proper(s(X)) = X >= X = s(proper(X))
      
      proper(0()) = 0 >= 0 = ok(0())
      
      proper(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(proper(X1),proper(X2))
      
      proper(head(X)) = X + 1 >= X + 1 = head(proper(X))
      
      proper(tail(X)) = X + 1 >= X + 1 = tail(proper(X))
      
      proper(if(X1,X2,X3)) = X1 + 1 >= X1 + 1 = if(proper(X1),proper(X2),proper(X3))
      
      proper(true()) = 0 >= 0 = ok(true())
      
      proper(false()) = 0 >= 0 = ok(false())
      
      proper(filter(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = filter(proper(X1),proper(X2))
      
      proper(divides(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = divides(proper(X1),proper(X2))
      
      sieve(ok(X)) = 0 >= 0 = ok(sieve(X))
      
      from(ok(X)) = 1 >= 0 = ok(from(X))
      
      s(ok(X)) = 0 >= 0 = ok(s(X))
      
      cons(ok(X1),ok(X2)) = 1 >= 0 = ok(cons(X1,X2))
      
      head(ok(X)) = 1 >= 0 = ok(head(X))
      
      tail(ok(X)) = 1 >= 0 = ok(tail(X))
      
      if(ok(X1),ok(X2),ok(X3)) = 1 >= 0 = ok(if(X1,X2,X3))
      
      filter(ok(X1),ok(X2)) = 1 >= 0 = ok(filter(X1,X2))
      
      divides(ok(X1),ok(X2)) = 1 >= 0 = ok(divides(X1,X2))
      
      top(mark(X)) = 0 >= 0 = top(proper(X))
      
      top(ok(X)) = 0 >= 0 = top(active(X))
     problem:
      DPs:
       active#(s(X)) -> active#(X)
       active#(sieve(X)) -> active#(X)
      TRS:
       active(primes()) -> mark(sieve(from(s(s(0())))))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(head(cons(X,Y))) -> mark(X)
       active(tail(cons(X,Y))) -> mark(Y)
       active(if(true(),X,Y)) -> mark(X)
       active(if(false(),X,Y)) -> mark(Y)
       active(filter(s(s(X)),cons(Y,Z))) ->
       mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
       active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
       active(sieve(X)) -> sieve(active(X))
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(head(X)) -> head(active(X))
       active(tail(X)) -> tail(active(X))
       active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
       active(filter(X1,X2)) -> filter(active(X1),X2)
       active(filter(X1,X2)) -> filter(X1,active(X2))
       active(divides(X1,X2)) -> divides(active(X1),X2)
       active(divides(X1,X2)) -> divides(X1,active(X2))
       sieve(mark(X)) -> mark(sieve(X))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       head(mark(X)) -> mark(head(X))
       tail(mark(X)) -> mark(tail(X))
       if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
       filter(mark(X1),X2) -> mark(filter(X1,X2))
       filter(X1,mark(X2)) -> mark(filter(X1,X2))
       divides(mark(X1),X2) -> mark(divides(X1,X2))
       divides(X1,mark(X2)) -> mark(divides(X1,X2))
       proper(primes()) -> ok(primes())
       proper(sieve(X)) -> sieve(proper(X))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(0()) -> ok(0())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(head(X)) -> head(proper(X))
       proper(tail(X)) -> tail(proper(X))
       proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
       proper(true()) -> ok(true())
       proper(false()) -> ok(false())
       proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
       proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
       sieve(ok(X)) -> ok(sieve(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       head(ok(X)) -> ok(head(X))
       tail(ok(X)) -> ok(tail(X))
       if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
       filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
       divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [active#](x0) = x0 + 1,
       
       [top](x0) = 1,
       
       [ok](x0) = x0,
       
       [proper](x0) = x0,
       
       [divides](x0, x1) = 0,
       
       [filter](x0, x1) = 0,
       
       [false] = 0,
       
       [if](x0, x1, x2) = 1,
       
       [true] = 0,
       
       [tail](x0) = 0,
       
       [head](x0) = 0,
       
       [cons](x0, x1) = 0,
       
       [mark](x0) = 0,
       
       [sieve](x0) = x0,
       
       [from](x0) = 1,
       
       [s](x0) = x0 + 1,
       
       [0] = 1,
       
       [active](x0) = x0,
       
       [primes] = 0
      orientation:
       active#(s(X)) = X + 2 >= X + 1 = active#(X)
       
       active#(sieve(X)) = X + 1 >= X + 1 = active#(X)
       
       active(primes()) = 0 >= 0 = mark(sieve(from(s(s(0())))))
       
       active(from(X)) = 1 >= 0 = mark(cons(X,from(s(X))))
       
       active(head(cons(X,Y))) = 0 >= 0 = mark(X)
       
       active(tail(cons(X,Y))) = 0 >= 0 = mark(Y)
       
       active(if(true(),X,Y)) = 1 >= 0 = mark(X)
       
       active(if(false(),X,Y)) = 1 >= 0 = mark(Y)
       
       active(filter(s(s(X)),cons(Y,Z))) = 0 >= 0 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
       
       active(sieve(cons(X,Y))) = 0 >= 0 = mark(cons(X,filter(X,sieve(Y))))
       
       active(sieve(X)) = X >= X = sieve(active(X))
       
       active(from(X)) = 1 >= 1 = from(active(X))
       
       active(s(X)) = X + 1 >= X + 1 = s(active(X))
       
       active(cons(X1,X2)) = 0 >= 0 = cons(active(X1),X2)
       
       active(head(X)) = 0 >= 0 = head(active(X))
       
       active(tail(X)) = 0 >= 0 = tail(active(X))
       
       active(if(X1,X2,X3)) = 1 >= 1 = if(active(X1),X2,X3)
       
       active(filter(X1,X2)) = 0 >= 0 = filter(active(X1),X2)
       
       active(filter(X1,X2)) = 0 >= 0 = filter(X1,active(X2))
       
       active(divides(X1,X2)) = 0 >= 0 = divides(active(X1),X2)
       
       active(divides(X1,X2)) = 0 >= 0 = divides(X1,active(X2))
       
       sieve(mark(X)) = 0 >= 0 = mark(sieve(X))
       
       from(mark(X)) = 1 >= 0 = mark(from(X))
       
       s(mark(X)) = 1 >= 0 = mark(s(X))
       
       cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2))
       
       head(mark(X)) = 0 >= 0 = mark(head(X))
       
       tail(mark(X)) = 0 >= 0 = mark(tail(X))
       
       if(mark(X1),X2,X3) = 1 >= 0 = mark(if(X1,X2,X3))
       
       filter(mark(X1),X2) = 0 >= 0 = mark(filter(X1,X2))
       
       filter(X1,mark(X2)) = 0 >= 0 = mark(filter(X1,X2))
       
       divides(mark(X1),X2) = 0 >= 0 = mark(divides(X1,X2))
       
       divides(X1,mark(X2)) = 0 >= 0 = mark(divides(X1,X2))
       
       proper(primes()) = 0 >= 0 = ok(primes())
       
       proper(sieve(X)) = X >= X = sieve(proper(X))
       
       proper(from(X)) = 1 >= 1 = from(proper(X))
       
       proper(s(X)) = X + 1 >= X + 1 = s(proper(X))
       
       proper(0()) = 1 >= 1 = ok(0())
       
       proper(cons(X1,X2)) = 0 >= 0 = cons(proper(X1),proper(X2))
       
       proper(head(X)) = 0 >= 0 = head(proper(X))
       
       proper(tail(X)) = 0 >= 0 = tail(proper(X))
       
       proper(if(X1,X2,X3)) = 1 >= 1 = if(proper(X1),proper(X2),proper(X3))
       
       proper(true()) = 0 >= 0 = ok(true())
       
       proper(false()) = 0 >= 0 = ok(false())
       
       proper(filter(X1,X2)) = 0 >= 0 = filter(proper(X1),proper(X2))
       
       proper(divides(X1,X2)) = 0 >= 0 = divides(proper(X1),proper(X2))
       
       sieve(ok(X)) = X >= X = ok(sieve(X))
       
       from(ok(X)) = 1 >= 1 = ok(from(X))
       
       s(ok(X)) = X + 1 >= X + 1 = ok(s(X))
       
       cons(ok(X1),ok(X2)) = 0 >= 0 = ok(cons(X1,X2))
       
       head(ok(X)) = 0 >= 0 = ok(head(X))
       
       tail(ok(X)) = 0 >= 0 = ok(tail(X))
       
       if(ok(X1),ok(X2),ok(X3)) = 1 >= 1 = ok(if(X1,X2,X3))
       
       filter(ok(X1),ok(X2)) = 0 >= 0 = ok(filter(X1,X2))
       
       divides(ok(X1),ok(X2)) = 0 >= 0 = ok(divides(X1,X2))
       
       top(mark(X)) = 1 >= 1 = top(proper(X))
       
       top(ok(X)) = 1 >= 1 = top(active(X))
      problem:
       DPs:
        active#(sieve(X)) -> active#(X)
       TRS:
        active(primes()) -> mark(sieve(from(s(s(0())))))
        active(from(X)) -> mark(cons(X,from(s(X))))
        active(head(cons(X,Y))) -> mark(X)
        active(tail(cons(X,Y))) -> mark(Y)
        active(if(true(),X,Y)) -> mark(X)
        active(if(false(),X,Y)) -> mark(Y)
        active(filter(s(s(X)),cons(Y,Z))) ->
        mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
        active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
        active(sieve(X)) -> sieve(active(X))
        active(from(X)) -> from(active(X))
        active(s(X)) -> s(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(head(X)) -> head(active(X))
        active(tail(X)) -> tail(active(X))
        active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
        active(filter(X1,X2)) -> filter(active(X1),X2)
        active(filter(X1,X2)) -> filter(X1,active(X2))
        active(divides(X1,X2)) -> divides(active(X1),X2)
        active(divides(X1,X2)) -> divides(X1,active(X2))
        sieve(mark(X)) -> mark(sieve(X))
        from(mark(X)) -> mark(from(X))
        s(mark(X)) -> mark(s(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        head(mark(X)) -> mark(head(X))
        tail(mark(X)) -> mark(tail(X))
        if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
        filter(mark(X1),X2) -> mark(filter(X1,X2))
        filter(X1,mark(X2)) -> mark(filter(X1,X2))
        divides(mark(X1),X2) -> mark(divides(X1,X2))
        divides(X1,mark(X2)) -> mark(divides(X1,X2))
        proper(primes()) -> ok(primes())
        proper(sieve(X)) -> sieve(proper(X))
        proper(from(X)) -> from(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(head(X)) -> head(proper(X))
        proper(tail(X)) -> tail(proper(X))
        proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
        proper(true()) -> ok(true())
        proper(false()) -> ok(false())
        proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
        proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
        sieve(ok(X)) -> ok(sieve(X))
        from(ok(X)) -> ok(from(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        head(ok(X)) -> ok(head(X))
        tail(ok(X)) -> ok(tail(X))
        if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
        filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
        divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [active#](x0) = x0 + 1,
        
        [top](x0) = 0,
        
        [ok](x0) = x0,
        
        [proper](x0) = x0,
        
        [divides](x0, x1) = 0,
        
        [filter](x0, x1) = 0,
        
        [false] = 0,
        
        [if](x0, x1, x2) = x0,
        
        [true] = 1,
        
        [tail](x0) = 0,
        
        [head](x0) = 0,
        
        [cons](x0, x1) = 0,
        
        [mark](x0) = 0,
        
        [sieve](x0) = x0 + 1,
        
        [from](x0) = 0,
        
        [s](x0) = 0,
        
        [0] = 0,
        
        [active](x0) = x0,
        
        [primes] = 0
       orientation:
        active#(sieve(X)) = X + 2 >= X + 1 = active#(X)
        
        active(primes()) = 0 >= 0 = mark(sieve(from(s(s(0())))))
        
        active(from(X)) = 0 >= 0 = mark(cons(X,from(s(X))))
        
        active(head(cons(X,Y))) = 0 >= 0 = mark(X)
        
        active(tail(cons(X,Y))) = 0 >= 0 = mark(Y)
        
        active(if(true(),X,Y)) = 1 >= 0 = mark(X)
        
        active(if(false(),X,Y)) = 0 >= 0 = mark(Y)
        
        active(filter(s(s(X)),cons(Y,Z))) = 0 >= 0 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
        
        active(sieve(cons(X,Y))) = 1 >= 0 = mark(cons(X,filter(X,sieve(Y))))
        
        active(sieve(X)) = X + 1 >= X + 1 = sieve(active(X))
        
        active(from(X)) = 0 >= 0 = from(active(X))
        
        active(s(X)) = 0 >= 0 = s(active(X))
        
        active(cons(X1,X2)) = 0 >= 0 = cons(active(X1),X2)
        
        active(head(X)) = 0 >= 0 = head(active(X))
        
        active(tail(X)) = 0 >= 0 = tail(active(X))
        
        active(if(X1,X2,X3)) = X1 >= X1 = if(active(X1),X2,X3)
        
        active(filter(X1,X2)) = 0 >= 0 = filter(active(X1),X2)
        
        active(filter(X1,X2)) = 0 >= 0 = filter(X1,active(X2))
        
        active(divides(X1,X2)) = 0 >= 0 = divides(active(X1),X2)
        
        active(divides(X1,X2)) = 0 >= 0 = divides(X1,active(X2))
        
        sieve(mark(X)) = 1 >= 0 = mark(sieve(X))
        
        from(mark(X)) = 0 >= 0 = mark(from(X))
        
        s(mark(X)) = 0 >= 0 = mark(s(X))
        
        cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2))
        
        head(mark(X)) = 0 >= 0 = mark(head(X))
        
        tail(mark(X)) = 0 >= 0 = mark(tail(X))
        
        if(mark(X1),X2,X3) = 0 >= 0 = mark(if(X1,X2,X3))
        
        filter(mark(X1),X2) = 0 >= 0 = mark(filter(X1,X2))
        
        filter(X1,mark(X2)) = 0 >= 0 = mark(filter(X1,X2))
        
        divides(mark(X1),X2) = 0 >= 0 = mark(divides(X1,X2))
        
        divides(X1,mark(X2)) = 0 >= 0 = mark(divides(X1,X2))
        
        proper(primes()) = 0 >= 0 = ok(primes())
        
        proper(sieve(X)) = X + 1 >= X + 1 = sieve(proper(X))
        
        proper(from(X)) = 0 >= 0 = from(proper(X))
        
        proper(s(X)) = 0 >= 0 = s(proper(X))
        
        proper(0()) = 0 >= 0 = ok(0())
        
        proper(cons(X1,X2)) = 0 >= 0 = cons(proper(X1),proper(X2))
        
        proper(head(X)) = 0 >= 0 = head(proper(X))
        
        proper(tail(X)) = 0 >= 0 = tail(proper(X))
        
        proper(if(X1,X2,X3)) = X1 >= X1 = if(proper(X1),proper(X2),proper(X3))
        
        proper(true()) = 1 >= 1 = ok(true())
        
        proper(false()) = 0 >= 0 = ok(false())
        
        proper(filter(X1,X2)) = 0 >= 0 = filter(proper(X1),proper(X2))
        
        proper(divides(X1,X2)) = 0 >= 0 = divides(proper(X1),proper(X2))
        
        sieve(ok(X)) = X + 1 >= X + 1 = ok(sieve(X))
        
        from(ok(X)) = 0 >= 0 = ok(from(X))
        
        s(ok(X)) = 0 >= 0 = ok(s(X))
        
        cons(ok(X1),ok(X2)) = 0 >= 0 = ok(cons(X1,X2))
        
        head(ok(X)) = 0 >= 0 = ok(head(X))
        
        tail(ok(X)) = 0 >= 0 = ok(tail(X))
        
        if(ok(X1),ok(X2),ok(X3)) = X1 >= X1 = ok(if(X1,X2,X3))
        
        filter(ok(X1),ok(X2)) = 0 >= 0 = ok(filter(X1,X2))
        
        divides(ok(X1),ok(X2)) = 0 >= 0 = ok(divides(X1,X2))
        
        top(mark(X)) = 0 >= 0 = top(proper(X))
        
        top(ok(X)) = 0 >= 0 = top(active(X))
       problem:
        DPs:
         
        TRS:
         active(primes()) -> mark(sieve(from(s(s(0())))))
         active(from(X)) -> mark(cons(X,from(s(X))))
         active(head(cons(X,Y))) -> mark(X)
         active(tail(cons(X,Y))) -> mark(Y)
         active(if(true(),X,Y)) -> mark(X)
         active(if(false(),X,Y)) -> mark(Y)
         active(filter(s(s(X)),cons(Y,Z))) ->
         mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
         active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
         active(sieve(X)) -> sieve(active(X))
         active(from(X)) -> from(active(X))
         active(s(X)) -> s(active(X))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(head(X)) -> head(active(X))
         active(tail(X)) -> tail(active(X))
         active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
         active(filter(X1,X2)) -> filter(active(X1),X2)
         active(filter(X1,X2)) -> filter(X1,active(X2))
         active(divides(X1,X2)) -> divides(active(X1),X2)
         active(divides(X1,X2)) -> divides(X1,active(X2))
         sieve(mark(X)) -> mark(sieve(X))
         from(mark(X)) -> mark(from(X))
         s(mark(X)) -> mark(s(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         head(mark(X)) -> mark(head(X))
         tail(mark(X)) -> mark(tail(X))
         if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
         filter(mark(X1),X2) -> mark(filter(X1,X2))
         filter(X1,mark(X2)) -> mark(filter(X1,X2))
         divides(mark(X1),X2) -> mark(divides(X1,X2))
         divides(X1,mark(X2)) -> mark(divides(X1,X2))
         proper(primes()) -> ok(primes())
         proper(sieve(X)) -> sieve(proper(X))
         proper(from(X)) -> from(proper(X))
         proper(s(X)) -> s(proper(X))
         proper(0()) -> ok(0())
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(head(X)) -> head(proper(X))
         proper(tail(X)) -> tail(proper(X))
         proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
         proper(true()) -> ok(true())
         proper(false()) -> ok(false())
         proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
         proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
         sieve(ok(X)) -> ok(sieve(X))
         from(ok(X)) -> ok(from(X))
         s(ok(X)) -> ok(s(X))
         cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
         head(ok(X)) -> ok(head(X))
         tail(ok(X)) -> ok(tail(X))
         if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
         filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
         divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
    
    DPs:
     sieve#(ok(X)) -> sieve#(X)
     sieve#(mark(X)) -> sieve#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     from#(ok(X)) -> from#(X)
     from#(mark(X)) -> from#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     s#(ok(X)) -> s#(X)
     s#(mark(X)) -> s#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     cons#(mark(X1),X2) -> cons#(X1,X2)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [cons#](x0, x1) = x1 + 1,
      
      [top](x0) = 1,
      
      [ok](x0) = x0 + 1,
      
      [proper](x0) = x0 + 1,
      
      [divides](x0, x1) = x1,
      
      [filter](x0, x1) = x0,
      
      [false] = 1,
      
      [if](x0, x1, x2) = x1,
      
      [true] = 0,
      
      [tail](x0) = x0,
      
      [head](x0) = x0,
      
      [cons](x0, x1) = x0,
      
      [mark](x0) = 0,
      
      [sieve](x0) = x0,
      
      [from](x0) = x0,
      
      [s](x0) = x0 + 1,
      
      [0] = 1,
      
      [active](x0) = x0,
      
      [primes] = 0
     orientation:
      cons#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = cons#(X1,X2)
      
      cons#(mark(X1),X2) = X2 + 1 >= X2 + 1 = cons#(X1,X2)
      
      active(primes()) = 0 >= 0 = mark(sieve(from(s(s(0())))))
      
      active(from(X)) = X >= 0 = mark(cons(X,from(s(X))))
      
      active(head(cons(X,Y))) = X >= 0 = mark(X)
      
      active(tail(cons(X,Y))) = X >= 0 = mark(Y)
      
      active(if(true(),X,Y)) = X >= 0 = mark(X)
      
      active(if(false(),X,Y)) = X >= 0 = mark(Y)
      
      active(filter(s(s(X)),cons(Y,Z))) = X + 2 >= 0 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
      
      active(sieve(cons(X,Y))) = X >= 0 = mark(cons(X,filter(X,sieve(Y))))
      
      active(sieve(X)) = X >= X = sieve(active(X))
      
      active(from(X)) = X >= X = from(active(X))
      
      active(s(X)) = X + 1 >= X + 1 = s(active(X))
      
      active(cons(X1,X2)) = X1 >= X1 = cons(active(X1),X2)
      
      active(head(X)) = X >= X = head(active(X))
      
      active(tail(X)) = X >= X = tail(active(X))
      
      active(if(X1,X2,X3)) = X2 >= X2 = if(active(X1),X2,X3)
      
      active(filter(X1,X2)) = X1 >= X1 = filter(active(X1),X2)
      
      active(filter(X1,X2)) = X1 >= X1 = filter(X1,active(X2))
      
      active(divides(X1,X2)) = X2 >= X2 = divides(active(X1),X2)
      
      active(divides(X1,X2)) = X2 >= X2 = divides(X1,active(X2))
      
      sieve(mark(X)) = 0 >= 0 = mark(sieve(X))
      
      from(mark(X)) = 0 >= 0 = mark(from(X))
      
      s(mark(X)) = 1 >= 0 = mark(s(X))
      
      cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2))
      
      head(mark(X)) = 0 >= 0 = mark(head(X))
      
      tail(mark(X)) = 0 >= 0 = mark(tail(X))
      
      if(mark(X1),X2,X3) = X2 >= 0 = mark(if(X1,X2,X3))
      
      filter(mark(X1),X2) = 0 >= 0 = mark(filter(X1,X2))
      
      filter(X1,mark(X2)) = X1 >= 0 = mark(filter(X1,X2))
      
      divides(mark(X1),X2) = X2 >= 0 = mark(divides(X1,X2))
      
      divides(X1,mark(X2)) = 0 >= 0 = mark(divides(X1,X2))
      
      proper(primes()) = 1 >= 1 = ok(primes())
      
      proper(sieve(X)) = X + 1 >= X + 1 = sieve(proper(X))
      
      proper(from(X)) = X + 1 >= X + 1 = from(proper(X))
      
      proper(s(X)) = X + 2 >= X + 2 = s(proper(X))
      
      proper(0()) = 2 >= 2 = ok(0())
      
      proper(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(proper(X1),proper(X2))
      
      proper(head(X)) = X + 1 >= X + 1 = head(proper(X))
      
      proper(tail(X)) = X + 1 >= X + 1 = tail(proper(X))
      
      proper(if(X1,X2,X3)) = X2 + 1 >= X2 + 1 = if(proper(X1),proper(X2),proper(X3))
      
      proper(true()) = 1 >= 1 = ok(true())
      
      proper(false()) = 2 >= 2 = ok(false())
      
      proper(filter(X1,X2)) = X1 + 1 >= X1 + 1 = filter(proper(X1),proper(X2))
      
      proper(divides(X1,X2)) = X2 + 1 >= X2 + 1 = divides(proper(X1),proper(X2))
      
      sieve(ok(X)) = X + 1 >= X + 1 = ok(sieve(X))
      
      from(ok(X)) = X + 1 >= X + 1 = ok(from(X))
      
      s(ok(X)) = X + 2 >= X + 2 = ok(s(X))
      
      cons(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(cons(X1,X2))
      
      head(ok(X)) = X + 1 >= X + 1 = ok(head(X))
      
      tail(ok(X)) = X + 1 >= X + 1 = ok(tail(X))
      
      if(ok(X1),ok(X2),ok(X3)) = X2 + 1 >= X2 + 1 = ok(if(X1,X2,X3))
      
      filter(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(filter(X1,X2))
      
      divides(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(divides(X1,X2))
      
      top(mark(X)) = 1 >= 1 = top(proper(X))
      
      top(ok(X)) = 1 >= 1 = top(active(X))
     problem:
      DPs:
       cons#(mark(X1),X2) -> cons#(X1,X2)
      TRS:
       active(primes()) -> mark(sieve(from(s(s(0())))))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(head(cons(X,Y))) -> mark(X)
       active(tail(cons(X,Y))) -> mark(Y)
       active(if(true(),X,Y)) -> mark(X)
       active(if(false(),X,Y)) -> mark(Y)
       active(filter(s(s(X)),cons(Y,Z))) ->
       mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
       active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
       active(sieve(X)) -> sieve(active(X))
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(head(X)) -> head(active(X))
       active(tail(X)) -> tail(active(X))
       active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
       active(filter(X1,X2)) -> filter(active(X1),X2)
       active(filter(X1,X2)) -> filter(X1,active(X2))
       active(divides(X1,X2)) -> divides(active(X1),X2)
       active(divides(X1,X2)) -> divides(X1,active(X2))
       sieve(mark(X)) -> mark(sieve(X))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       head(mark(X)) -> mark(head(X))
       tail(mark(X)) -> mark(tail(X))
       if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
       filter(mark(X1),X2) -> mark(filter(X1,X2))
       filter(X1,mark(X2)) -> mark(filter(X1,X2))
       divides(mark(X1),X2) -> mark(divides(X1,X2))
       divides(X1,mark(X2)) -> mark(divides(X1,X2))
       proper(primes()) -> ok(primes())
       proper(sieve(X)) -> sieve(proper(X))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(0()) -> ok(0())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(head(X)) -> head(proper(X))
       proper(tail(X)) -> tail(proper(X))
       proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
       proper(true()) -> ok(true())
       proper(false()) -> ok(false())
       proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
       proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
       sieve(ok(X)) -> ok(sieve(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       head(ok(X)) -> ok(head(X))
       tail(ok(X)) -> ok(tail(X))
       if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
       filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
       divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Open
    
    DPs:
     head#(ok(X)) -> head#(X)
     head#(mark(X)) -> head#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     tail#(ok(X)) -> tail#(X)
     tail#(mark(X)) -> tail#(X)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
     if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [if#](x0, x1, x2) = x1 + x2,
      
      [top](x0) = 0,
      
      [ok](x0) = x0 + 1,
      
      [proper](x0) = x0 + 1,
      
      [divides](x0, x1) = x1,
      
      [filter](x0, x1) = x0 + 1,
      
      [false] = 0,
      
      [if](x0, x1, x2) = x0,
      
      [true] = 0,
      
      [tail](x0) = x0,
      
      [head](x0) = x0 + 1,
      
      [cons](x0, x1) = x0 + 1,
      
      [mark](x0) = 0,
      
      [sieve](x0) = x0,
      
      [from](x0) = x0 + 1,
      
      [s](x0) = x0,
      
      [0] = 1,
      
      [active](x0) = x0,
      
      [primes] = 0
     orientation:
      if#(ok(X1),ok(X2),ok(X3)) = X2 + X3 + 2 >= X2 + X3 = if#(X1,X2,X3)
      
      if#(mark(X1),X2,X3) = X2 + X3 >= X2 + X3 = if#(X1,X2,X3)
      
      active(primes()) = 0 >= 0 = mark(sieve(from(s(s(0())))))
      
      active(from(X)) = X + 1 >= 0 = mark(cons(X,from(s(X))))
      
      active(head(cons(X,Y))) = X + 2 >= 0 = mark(X)
      
      active(tail(cons(X,Y))) = X + 1 >= 0 = mark(Y)
      
      active(if(true(),X,Y)) = 0 >= 0 = mark(X)
      
      active(if(false(),X,Y)) = 0 >= 0 = mark(Y)
      
      active(filter(s(s(X)),cons(Y,Z))) = X + 1 >= 0 = mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
      
      active(sieve(cons(X,Y))) = X + 1 >= 0 = mark(cons(X,filter(X,sieve(Y))))
      
      active(sieve(X)) = X >= X = sieve(active(X))
      
      active(from(X)) = X + 1 >= X + 1 = from(active(X))
      
      active(s(X)) = X >= X = s(active(X))
      
      active(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(active(X1),X2)
      
      active(head(X)) = X + 1 >= X + 1 = head(active(X))
      
      active(tail(X)) = X >= X = tail(active(X))
      
      active(if(X1,X2,X3)) = X1 >= X1 = if(active(X1),X2,X3)
      
      active(filter(X1,X2)) = X1 + 1 >= X1 + 1 = filter(active(X1),X2)
      
      active(filter(X1,X2)) = X1 + 1 >= X1 + 1 = filter(X1,active(X2))
      
      active(divides(X1,X2)) = X2 >= X2 = divides(active(X1),X2)
      
      active(divides(X1,X2)) = X2 >= X2 = divides(X1,active(X2))
      
      sieve(mark(X)) = 0 >= 0 = mark(sieve(X))
      
      from(mark(X)) = 1 >= 0 = mark(from(X))
      
      s(mark(X)) = 0 >= 0 = mark(s(X))
      
      cons(mark(X1),X2) = 1 >= 0 = mark(cons(X1,X2))
      
      head(mark(X)) = 1 >= 0 = mark(head(X))
      
      tail(mark(X)) = 0 >= 0 = mark(tail(X))
      
      if(mark(X1),X2,X3) = 0 >= 0 = mark(if(X1,X2,X3))
      
      filter(mark(X1),X2) = 1 >= 0 = mark(filter(X1,X2))
      
      filter(X1,mark(X2)) = X1 + 1 >= 0 = mark(filter(X1,X2))
      
      divides(mark(X1),X2) = X2 >= 0 = mark(divides(X1,X2))
      
      divides(X1,mark(X2)) = 0 >= 0 = mark(divides(X1,X2))
      
      proper(primes()) = 1 >= 1 = ok(primes())
      
      proper(sieve(X)) = X + 1 >= X + 1 = sieve(proper(X))
      
      proper(from(X)) = X + 2 >= X + 2 = from(proper(X))
      
      proper(s(X)) = X + 1 >= X + 1 = s(proper(X))
      
      proper(0()) = 2 >= 2 = ok(0())
      
      proper(cons(X1,X2)) = X1 + 2 >= X1 + 2 = cons(proper(X1),proper(X2))
      
      proper(head(X)) = X + 2 >= X + 2 = head(proper(X))
      
      proper(tail(X)) = X + 1 >= X + 1 = tail(proper(X))
      
      proper(if(X1,X2,X3)) = X1 + 1 >= X1 + 1 = if(proper(X1),proper(X2),proper(X3))
      
      proper(true()) = 1 >= 1 = ok(true())
      
      proper(false()) = 1 >= 1 = ok(false())
      
      proper(filter(X1,X2)) = X1 + 2 >= X1 + 2 = filter(proper(X1),proper(X2))
      
      proper(divides(X1,X2)) = X2 + 1 >= X2 + 1 = divides(proper(X1),proper(X2))
      
      sieve(ok(X)) = X + 1 >= X + 1 = ok(sieve(X))
      
      from(ok(X)) = X + 2 >= X + 2 = ok(from(X))
      
      s(ok(X)) = X + 1 >= X + 1 = ok(s(X))
      
      cons(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(cons(X1,X2))
      
      head(ok(X)) = X + 2 >= X + 2 = ok(head(X))
      
      tail(ok(X)) = X + 1 >= X + 1 = ok(tail(X))
      
      if(ok(X1),ok(X2),ok(X3)) = X1 + 1 >= X1 + 1 = ok(if(X1,X2,X3))
      
      filter(ok(X1),ok(X2)) = X1 + 2 >= X1 + 2 = ok(filter(X1,X2))
      
      divides(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(divides(X1,X2))
      
      top(mark(X)) = 0 >= 0 = top(proper(X))
      
      top(ok(X)) = 0 >= 0 = top(active(X))
     problem:
      DPs:
       if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
      TRS:
       active(primes()) -> mark(sieve(from(s(s(0())))))
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(head(cons(X,Y))) -> mark(X)
       active(tail(cons(X,Y))) -> mark(Y)
       active(if(true(),X,Y)) -> mark(X)
       active(if(false(),X,Y)) -> mark(Y)
       active(filter(s(s(X)),cons(Y,Z))) ->
       mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
       active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
       active(sieve(X)) -> sieve(active(X))
       active(from(X)) -> from(active(X))
       active(s(X)) -> s(active(X))
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(head(X)) -> head(active(X))
       active(tail(X)) -> tail(active(X))
       active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
       active(filter(X1,X2)) -> filter(active(X1),X2)
       active(filter(X1,X2)) -> filter(X1,active(X2))
       active(divides(X1,X2)) -> divides(active(X1),X2)
       active(divides(X1,X2)) -> divides(X1,active(X2))
       sieve(mark(X)) -> mark(sieve(X))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       head(mark(X)) -> mark(head(X))
       tail(mark(X)) -> mark(tail(X))
       if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
       filter(mark(X1),X2) -> mark(filter(X1,X2))
       filter(X1,mark(X2)) -> mark(filter(X1,X2))
       divides(mark(X1),X2) -> mark(divides(X1,X2))
       divides(X1,mark(X2)) -> mark(divides(X1,X2))
       proper(primes()) -> ok(primes())
       proper(sieve(X)) -> sieve(proper(X))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
       proper(0()) -> ok(0())
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(head(X)) -> head(proper(X))
       proper(tail(X)) -> tail(proper(X))
       proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
       proper(true()) -> ok(true())
       proper(false()) -> ok(false())
       proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
       proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
       sieve(ok(X)) -> ok(sieve(X))
       from(ok(X)) -> ok(from(X))
       s(ok(X)) -> ok(s(X))
       cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
       head(ok(X)) -> ok(head(X))
       tail(ok(X)) -> ok(tail(X))
       if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
       filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
       divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
       top(mark(X)) -> top(proper(X))
       top(ok(X)) -> top(active(X))
     Open
    
    DPs:
     filter#(ok(X1),ok(X2)) -> filter#(X1,X2)
     filter#(X1,mark(X2)) -> filter#(X1,X2)
     filter#(mark(X1),X2) -> filter#(X1,X2)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open
    
    DPs:
     divides#(ok(X1),ok(X2)) -> divides#(X1,X2)
     divides#(X1,mark(X2)) -> divides#(X1,X2)
     divides#(mark(X1),X2) -> divides#(X1,X2)
    TRS:
     active(primes()) -> mark(sieve(from(s(s(0())))))
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(head(cons(X,Y))) -> mark(X)
     active(tail(cons(X,Y))) -> mark(Y)
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     active(filter(s(s(X)),cons(Y,Z))) ->
     mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
     active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
     active(sieve(X)) -> sieve(active(X))
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(head(X)) -> head(active(X))
     active(tail(X)) -> tail(active(X))
     active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
     active(filter(X1,X2)) -> filter(active(X1),X2)
     active(filter(X1,X2)) -> filter(X1,active(X2))
     active(divides(X1,X2)) -> divides(active(X1),X2)
     active(divides(X1,X2)) -> divides(X1,active(X2))
     sieve(mark(X)) -> mark(sieve(X))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     head(mark(X)) -> mark(head(X))
     tail(mark(X)) -> mark(tail(X))
     if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
     filter(mark(X1),X2) -> mark(filter(X1,X2))
     filter(X1,mark(X2)) -> mark(filter(X1,X2))
     divides(mark(X1),X2) -> mark(divides(X1,X2))
     divides(X1,mark(X2)) -> mark(divides(X1,X2))
     proper(primes()) -> ok(primes())
     proper(sieve(X)) -> sieve(proper(X))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(head(X)) -> head(proper(X))
     proper(tail(X)) -> tail(proper(X))
     proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
     proper(true()) -> ok(true())
     proper(false()) -> ok(false())
     proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
     proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
     sieve(ok(X)) -> ok(sieve(X))
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     head(ok(X)) -> ok(head(X))
     tail(ok(X)) -> ok(tail(X))
     if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
     filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
     divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    Open