NO
Input TRS:
      1: primes() -> sieve(from(s(s(0()))))
      2: from(X) -> cons(X,n__from(s(X)))
      3: head(cons(X,Y)) -> X
      4: tail(cons(X,Y)) -> activate(Y)
      5: if(true(),X,Y) -> activate(X)
      6: if(false(),X,Y) -> activate(Y)
      7: filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
      8: sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
      9: from(X) -> n__from(X)
      10: filter(X1,X2) -> n__filter(X1,X2)
      11: cons(X1,X2) -> n__cons(X1,X2)
      12: activate(n__from(X)) -> from(X)
      13: activate(n__filter(X1,X2)) -> filter(X1,X2)
      14: activate(n__cons(X1,X2)) -> cons(X1,X2)
      15: activate(X) -> X
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Uncurrying if
      1: primes() -> sieve(from(s(s(0()))))
      2: from(X) -> cons(X,n__from(s(X)))
      3: head(cons(X,Y)) -> X
      4: tail(cons(X,Y)) -> activate(Y)
      5: if^1_true(X,Y) -> activate(X)
      6: if^1_false(X,Y) -> activate(Y)
      7: filter(s(s(X)),cons(Y,Z)) -> if^1_divides(s(s(X)),Y,n__filter(s(s(X)),activate(Z)),n__cons(Y,n__filter(X,sieve(Y))))
      8: sieve(cons(X,Y)) -> cons(X,n__filter(X,sieve(activate(Y))))
      9: from(X) -> n__from(X)
      10: filter(X1,X2) -> n__filter(X1,X2)
      11: cons(X1,X2) -> n__cons(X1,X2)
      12: activate(n__from(X)) -> from(X)
      13: activate(n__filter(X1,X2)) -> filter(X1,X2)
      14: activate(n__cons(X1,X2)) -> cons(X1,X2)
      15: activate(X) -> X
      16: if(false(),_2,_3) ->= if^1_false(_2,_3)
      17: if(divides(_1,_2),_4,_5) ->= if^1_divides(_1,_2,_4,_5)
      18: if(true(),_2,_3) ->= if^1_true(_2,_3)
Number of strict rules: 15
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #from(X) -> #cons(X,n__from(s(X)))
     #2: #if^1_false(X,Y) -> #activate(Y)
     #3: #activate(n__filter(X1,X2)) -> #filter(X1,X2)
     #4: #activate(n__from(X)) -> #from(X)
     #5: #activate(n__cons(X1,X2)) -> #cons(X1,X2)
     #6: #filter(s(s(X)),cons(Y,Z)) -> #activate(Z)
     #7: #filter(s(s(X)),cons(Y,Z)) -> #sieve(Y)
     #8: #if^1_true(X,Y) -> #activate(X)
     #9: #if(false(),_2,_3) ->? #if^1_false(_2,_3)
     #10: #primes() -> #sieve(from(s(s(0()))))
     #11: #primes() -> #from(s(s(0())))
     #12: #sieve(cons(X,Y)) -> #cons(X,n__filter(X,sieve(activate(Y))))
     #13: #sieve(cons(X,Y)) -> #sieve(activate(Y))
     #14: #sieve(cons(X,Y)) -> #activate(Y)
     #15: #tail(cons(X,Y)) -> #activate(Y)
     #16: #if(true(),_2,_3) ->? #if^1_true(_2,_3)
Number of SCCs: 1, DPs: 5
  SCC { #3 #6 #7 #13 #14 }
POLO(Sum)... succeeded.
      #cons	w: 0
      s 	w: 0
      #if^1_false	w: 0
      if^1_divides	w: 0
      activate	w: x1 + 5394
      #filter	w: x2
      n__from	w: x1 + 39468
      #activate	w: x1 + 5393
      false	w: 0
      #head	w: 0
      #primes	w: 0
      true	w: 0
      if^1_false	w: 0
      tail	w: 0
      0 	w: 0
      if	w: 0
      from	w: x1 + 44862
      n__cons	w: x1 + x2 + 2085
      n__filter	w: x2 + 2973
      #tail	w: 0
      sieve	w: 44083
      #from	w: 0
      head	w: 0
      cons	w: x1 + x2 + 5394
      #if	w: 0
      filter	w: x2 + 2973
      primes	w: 0
      #sieve	w: x1 + 5393
      #if^1_true	w: 0
      divides	w: 0
      if^1_true	w: 0
    USABLE RULES: { 2 7 9..15 }
    Removed DPs: #3 #6 #7 #14
Number of SCCs: 1, DPs: 1
  SCC { #13 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #sieve(cons(X,n__from(X_{1})))	-#13->
  #sieve(activate(n__from(X_{1})))	--->*
  #sieve(cons(X_{1},n__from(s(X_{1}))))
  Looping with: [ X := X_{1}; X_{1} := s(X_{1}); ]