Input TRS:
    1: f(n__f(n__a())) -> f(n__g(n__f(n__a())))
    2: f(X) -> n__f(X)
    3: a() -> n__a()
    4: g(X) -> n__g(X)
    5: activate(n__f(X)) -> f(X)
    6: activate(n__a()) -> a()
    7: activate(n__g(X)) -> g(activate(X))
    8: activate(X) -> X
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... removes: 8 5 6 2
     a()	weight: 0
  n__a()	weight: 0
activate(x1)	weight: (/ 22585 2) + 2 * x1
     f(x1)	weight: 11798 + x1
  n__f(x1)	weight: (/ 23595 2) + x1
  n__g(x1)	weight: x1
     g(x1)	weight: x1
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
1: f❆1_n__f(n__a()) -> f❆1_n__g(n__f(n__a()))
3: a() -> n__a()
4: g(X) -> n__g(X)
7: activate(n__g(X)) -> g(activate(X))
9: f(n__f(_1)) ->= f❆1_n__f(_1)
10: f(n__g(_1)) ->= f❆1_n__g(_1)
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 1 10 9
     a()	weight: 0
  n__a()	weight: 0
f❆1_n__f(x1)	weight: (/ 3 4) + x1
f❆1_n__g(x1)	weight: 2 * x1
activate(x1)	weight: (/ 30877 4) + x1
     f(x1)	weight: (/ 1 2) + 2 * x1
  n__f(x1)	weight: (/ 1 4) + x1
  n__g(x1)	weight: (/ 84953 4) + x1
     g(x1)	weight: (/ 84953 4) + x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4 7
     a()	weight: 0
  n__a()	weight: 0
f❆1_n__f(x1)	weight: (/ 3 4) + x1
f❆1_n__g(x1)	weight: 2 * x1
activate(x1)	weight: (/ 1 4) + 2 * x1
     f(x1)	weight: (/ 1 2) + 2 * x1
  n__f(x1)	weight: (/ 1 4) + x1
  n__g(x1)	weight: (/ 84953 4) + x1
     g(x1)	weight: (/ 42477 2) + x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
Number of SCCs: 0, DPs: 0, edges: 0
YES