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}
 LMPO:
  Quasi-Precedence:
  activate > h, 
  activate > f
  empty
  
Normal:
   pi(activate) = [1]
  
Safe:
   pi(h) = [1], pi(f) = [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