Input TRS:
    1: f(X) -> g(n__h(n__f(X)))
    2: h(X) -> n__h(X)
    3: f(X) -> n__f(X)
    4: activate(n__h(X)) -> h(activate(X))
    5: activate(n__f(X)) -> f(activate(X))
    6: activate(X) -> X
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 6
     h(x1)	weight: x1
  n__h(x1)	weight: x1
activate(x1)	weight: (/ 1 4) + x1
     f(x1)	weight: (/ 82609 4) + x1
  n__f(x1)	weight: (/ 82609 4) + x1
     g(x1)	weight: x1
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 1 3 5
     h(x1)	weight: x1
  n__h(x1)	weight: x1
activate(x1)	weight: (/ 1 4) + 2 * x1
     f(x1)	weight: (/ 2251 4) + x1
  n__f(x1)	weight: (/ 563 2) + x1
     g(x1)	weight: x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 4 2
     h(x1)	weight: (/ 3 16) + x1
  n__h(x1)	weight: (/ 1 8) + x1
activate(x1)	weight: (/ 1 16) + 2 * x1
     f(x1)	weight: (/ 1 4) + x1
  n__f(x1)	weight: (/ 1 8) + x1
     g(x1)	weight: x1
Number of strict rules: 0
YES