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