Input TRS:
    1: primes() -> sieve(from(s(s(0()))))
    2: from(X) -> cons(X,n__from(n__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(n__s(n__s(X)),activate(Z)),n__cons(Y,n__filter(X,n__sieve(Y))))
    8: sieve(cons(X,Y)) -> cons(X,n__filter(X,n__sieve(activate(Y))))
    9: from(X) -> n__from(X)
    10: s(X) -> n__s(X)
    11: filter(X1,X2) -> n__filter(X1,X2)
    12: cons(X1,X2) -> n__cons(X1,X2)
    13: sieve(X) -> n__sieve(X)
    14: activate(n__from(X)) -> from(activate(X))
    15: activate(n__s(X)) -> s(activate(X))
    16: activate(n__filter(X1,X2)) -> filter(activate(X1),activate(X2))
    17: activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
    18: activate(n__sieve(X)) -> sieve(activate(X))
    19: activate(X) -> X
Number of strict rules: 19
Direct Order(PosReal,>,Poly) ... failed.
Freezing if
1: primes() -> sieve(from(s(s(0()))))
2: from(X) -> cons(X,n__from(n__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(n__s(n__s(X)),activate(Z)),n__cons(Y,n__filter(X,n__sieve(Y))))
8: sieve(cons(X,Y)) -> cons(X,n__filter(X,n__sieve(activate(Y))))
9: from(X) -> n__from(X)
10: s(X) -> n__s(X)
11: filter(X1,X2) -> n__filter(X1,X2)
12: cons(X1,X2) -> n__cons(X1,X2)
13: sieve(X) -> n__sieve(X)
14: activate(n__from(X)) -> from(activate(X))
15: activate(n__s(X)) -> s(activate(X))
16: activate(n__filter(X1,X2)) -> filter(activate(X1),activate(X2))
17: activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
18: activate(n__sieve(X)) -> sieve(activate(X))
19: activate(X) -> X
20: if(false(),_2,_3) ->= if❆1_false(_2,_3)
21: if(divides(_1,_2),_4,_5) ->= if❆1_divides(_1,_2,_4,_5)
22: if(true(),_2,_3) ->= if❆1_true(_2,_3)
Number of strict rules: 19
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #from(X) -> #cons(X,n__from(n__s(X)))
   #2: #if❆1_false(X,Y) -> #activate(Y)
   #3: #activate(n__from(X)) -> #from(activate(X))
   #4: #activate(n__from(X)) -> #activate(X)
   #5: #if(false(),_2,_3) ->? #if❆1_false(_2,_3)
   #6: #filter(s(s(X)),cons(Y,Z)) -> #activate(Z)
   #7: #if❆1_true(X,Y) -> #activate(X)
   #8: #if(true(),_2,_3) ->? #if❆1_true(_2,_3)
   #9: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2)
   #10: #activate(n__cons(X1,X2)) -> #activate(X1)
   #11: #activate(n__filter(X1,X2)) -> #filter(activate(X1),activate(X2))
   #12: #activate(n__filter(X1,X2)) -> #activate(X1)
   #13: #activate(n__filter(X1,X2)) -> #activate(X2)
   #14: #primes() -> #sieve(from(s(s(0()))))
   #15: #primes() -> #from(s(s(0())))
   #16: #primes() -> #s(s(0()))
   #17: #primes() -> #s(0())
   #18: #sieve(cons(X,Y)) -> #cons(X,n__filter(X,n__sieve(activate(Y))))
   #19: #sieve(cons(X,Y)) -> #activate(Y)
   #20: #activate(n__s(X)) -> #s(activate(X))
   #21: #activate(n__s(X)) -> #activate(X)
   #22: #tail(cons(X,Y)) -> #activate(Y)
   #23: #activate(n__sieve(X)) -> #sieve(activate(X))
   #24: #activate(n__sieve(X)) -> #activate(X)
Number of SCCs: 1, DPs: 10, edges: 66
	SCC { #4 #6 #10..13 #19 #21 #23 #24 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
activate(x1)	weight: x1
#filter(x1,x2)	weight: max{0, (/ 1 8) + x2}
n__from(x1)	weight: (/ 3 8) + x1
#activate(x1)	weight: (/ 1 8) + 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
  n__s(x1)	weight: x1
  tail(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
  from(x1)	weight: (/ 3 8) + x1
   #s(x1)	weight: 0
n__cons(x1,x2)	weight: max{x2, (/ 3 8) + x1}
n__filter(x1,x2)	weight: max{x2, (/ 1 8) + x1}
#tail(x1)	weight: 0
if❆1_divides(x1,x2,x3,x4)	weight: max{0, x4}
 sieve(x1)	weight: (/ 1 4) + x1
if❆1_true(x1,x2)	weight: 0
n__sieve(x1)	weight: (/ 1 4) + x1
#from(x1)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: max{x2, (/ 3 8) + x1}
  #if(x1,x2,x3)	weight: 0
#if❆1_true(x1,x2)	weight: 0
filter(x1,x2)	weight: max{x2, (/ 1 8) + x1}
primes()	weight: 0
#sieve(x1)	weight: (/ 1 4) + x1
divides(x1,x2)	weight: 0
    Usable rules: { 2 7..19 }
    Removed DPs: #4 #10 #12 #19 #23 #24
Number of SCCs: 1, DPs: 4, edges: 10
	SCC { #6 #11 #13 #21 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
activate(x1)	weight: (/ 1 2) + x1
#filter(x1,x2)	weight: x2
n__from(x1)	weight: 0
#activate(x1)	weight: (/ 1 4) + 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
  n__s(x1)	weight: (/ 1 4) + x1
  tail(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
  from(x1)	weight: (/ 1 2)
   #s(x1)	weight: 0
n__cons(x1,x2)	weight: 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: (/ 3 4)
if❆1_true(x1,x2)	weight: 0
n__sieve(x1)	weight: (/ 1 4)
#from(x1)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + 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: 0
divides(x1,x2)	weight: 0
    Usable rules: { 2 7..19 }
    Removed DPs: #13 #21
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #6 #11 }
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...  failed.
MAYBE