TRS:
 {             f(X) -> g(n__h(n__f(X))),
               h(X) -> n__h(X),
               f(X) -> n__f(X),
  activate(n__h(X)) -> h(activate(X)),
  activate(n__f(X)) -> f(activate(X)),
        activate(X) -> X}
 POP*:
  Precedence:
  h > n__h, 
  f > n__f, 
  f > n__h, 
  f > g, 
  activate > h, 
  activate > f
  empty
  
Normal:
   pi(activate) = [1]
  
Safe:
   pi(h) = [1], pi(f) = [1], pi(n__f) = [1], pi(n__h) = [1], pi(g) = [1]
  
Predicative System:
   {              f(;X) -> g(;n__h(;n__f(;X))),
                  h(;X) -> n__h(;X),
                  f(;X) -> n__f(;X),
    activate(n__h(;X);) -> h(;activate(X;)),
    activate(n__f(;X);) -> f(;activate(X;)),
           activate(X;) -> X}
  Qed