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 Order(PosReal,>,Poly) ... failed.
Freezing 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 Order(PosReal,>,Poly) ... 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, edges: 8
	SCC { #3 #6 #7 #13 #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
activate(x1)	weight: (/ 1 4) + x1
#filter(x1,x2)	weight: x2
n__from(x1)	weight: (/ 1 4) + x1
#activate(x1)	weight: x1
 false()	weight: 0
#head(x1)	weight: 0
if❆1_false(x1,x2)	weight: 0
#if❆1_false(x1,x2)	weight: 0
#primes()	weight: 0
  true()	weight: 0
  tail(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
  from(x1)	weight: (/ 1 2) + x1
n__cons(x1,x2)	weight: (/ 1 4) + x1 + x2
n__filter(x1,x2)	weight: (/ 1 4) + x2
#tail(x1)	weight: 0
if❆1_divides(x1,x2,x3,x4)	weight: 0
 sieve(x1)	weight: (/ 1 4)
if❆1_true(x1,x2)	weight: 0
#from(x1)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
  #if(x1,x2,x3)	weight: 0
#if❆1_true(x1,x2)	weight: 0
filter(x1,x2)	weight: (/ 1 4) + x2
primes()	weight: 0
#sieve(x1)	weight: x1
divides(x1,x2)	weight: 0
    Usable rules: { 2 7 9..15 }
    Removed DPs: #3 #6 #7 #14
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: 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}); ]
NO