YES
TRS:
 {             f(X) -> g(n__h(n__f(X))),
               f(X) -> n__f(X),
               h(X) -> n__h(X),
        activate(X) -> X,
  activate(n__h(X)) -> h(activate(X)),
  activate(n__f(X)) -> f(activate(X))}
 DP:
  Strict:
   {activate#(n__h(X)) -> h#(activate(X)),
    activate#(n__h(X)) -> activate#(X),
    activate#(n__f(X)) -> f#(activate(X)),
    activate#(n__f(X)) -> activate#(X)}
  Weak:
  {             f(X) -> g(n__h(n__f(X))),
                f(X) -> n__f(X),
                h(X) -> n__h(X),
         activate(X) -> X,
   activate(n__h(X)) -> h(activate(X)),
   activate(n__f(X)) -> f(activate(X))}
  EDG:
   {(activate#(n__f(X)) -> activate#(X), activate#(n__f(X)) -> activate#(X))
    (activate#(n__f(X)) -> activate#(X), activate#(n__f(X)) -> f#(activate(X)))
    (activate#(n__f(X)) -> activate#(X), activate#(n__h(X)) -> activate#(X))
    (activate#(n__f(X)) -> activate#(X), activate#(n__h(X)) -> h#(activate(X)))
    (activate#(n__h(X)) -> activate#(X), activate#(n__h(X)) -> h#(activate(X)))
    (activate#(n__h(X)) -> activate#(X), activate#(n__h(X)) -> activate#(X))
    (activate#(n__h(X)) -> activate#(X), activate#(n__f(X)) -> f#(activate(X)))
    (activate#(n__h(X)) -> activate#(X), activate#(n__f(X)) -> activate#(X))}
   SCCS:
    Scc:
     {activate#(n__h(X)) -> activate#(X),
      activate#(n__f(X)) -> activate#(X)}
    SCC:
     Strict:
      {activate#(n__h(X)) -> activate#(X),
       activate#(n__f(X)) -> activate#(X)}
     Weak:
     {             f(X) -> g(n__h(n__f(X))),
                   f(X) -> n__f(X),
                   h(X) -> n__h(X),
            activate(X) -> X,
      activate(n__h(X)) -> h(activate(X)),
      activate(n__f(X)) -> f(activate(X))}
     SPSC:
      Simple Projection:
       pi(activate#) = 0
      Strict:
       {activate#(n__f(X)) -> activate#(X)}
      EDG:
       {(activate#(n__f(X)) -> activate#(X), activate#(n__f(X)) -> activate#(X))}
       SCCS:
        Scc:
         {activate#(n__f(X)) -> activate#(X)}
        SCC:
         Strict:
          {activate#(n__f(X)) -> activate#(X)}
         Weak:
         {             f(X) -> g(n__h(n__f(X))),
                       f(X) -> n__f(X),
                       h(X) -> n__h(X),
                activate(X) -> X,
          activate(n__h(X)) -> h(activate(X)),
          activate(n__f(X)) -> f(activate(X))}
         SPSC:
          Simple Projection:
           pi(activate#) = 0
          Strict:
           {}
          Qed