Input TRS:
    1: f(X) -> cons(X,n__f(n__g(X)))
    2: g(0()) -> s(0())
    3: g(s(X)) -> s(s(g(X)))
    4: sel(0(),cons(X,Y)) -> X
    5: sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
    6: f(X) -> n__f(X)
    7: g(X) -> n__g(X)
    8: activate(n__f(X)) -> f(activate(X))
    9: activate(n__g(X)) -> g(activate(X))
    10: activate(X) -> X
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #activate(n__g(X)) -> #g(activate(X))
   #2: #activate(n__g(X)) -> #activate(X)
   #3: #sel(s(X),cons(Y,Z)) -> #sel(X,activate(Z))
   #4: #sel(s(X),cons(Y,Z)) -> #activate(Z)
   #5: #g(s(X)) -> #g(X)
   #6: #activate(n__f(X)) -> #f(activate(X))
   #7: #activate(n__f(X)) -> #activate(X)
Number of SCCs: 3, DPs: 4, edges: 6
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
activate(x1)	weight: 0
#activate(x1)	weight: 0
     f(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
  n__f(x1)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: x1
  n__g(x1)	weight: 0
  cons(x1,x2)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 3, edges: 5
	SCC { #2 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2)
activate(x1)	weight: 0
#activate(x1)	weight: x1
     f(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
  n__f(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
  n__g(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #7
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
activate(x1)	weight: (/ 1 16) + x1
#activate(x1)	weight: 0
     f(x1)	weight: x1
     0()	weight: 0
 #sel(x1,x2)	weight: x1
   sel(x1,x2)	weight: 0
  n__f(x1)	weight: (/ 1 16) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
  n__g(x1)	weight: (/ 1 16) + x1
  cons(x1,x2)	weight: (/ 1 16) + x2
     g(x1)	weight: (/ 3 16)
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES