YES
TRS:
 {             c(X) -> d(activate(X)),
               f(X) -> n__f(X),
            f(f(X)) -> c(n__f(g(n__f(X)))),
               d(X) -> n__d(X),
        activate(X) -> X,
  activate(n__f(X)) -> f(X),
  activate(n__d(X)) -> d(X),
               h(X) -> c(n__d(X))}
 RUF:
  Strict:
   {             c(X) -> d(activate(X)),
                 f(X) -> n__f(X),
              f(f(X)) -> c(n__f(g(n__f(X)))),
                 d(X) -> n__d(X),
          activate(X) -> X,
    activate(n__f(X)) -> f(X),
    activate(n__d(X)) -> d(X)}
  Weak:
   {}
  DP:
   Strict:
    {             c#(X) -> d#(activate(X)),
                  c#(X) -> activate#(X),
               f#(f(X)) -> c#(n__f(g(n__f(X)))),
     activate#(n__f(X)) -> f#(X),
     activate#(n__d(X)) -> d#(X)}
   Weak:
   {             c(X) -> d(activate(X)),
                 f(X) -> n__f(X),
              f(f(X)) -> c(n__f(g(n__f(X)))),
                 d(X) -> n__d(X),
          activate(X) -> X,
    activate(n__f(X)) -> f(X),
    activate(n__d(X)) -> d(X)}
   EDG:
    {(activate#(n__f(X)) -> f#(X), f#(f(X)) -> c#(n__f(g(n__f(X)))))
     (f#(f(X)) -> c#(n__f(g(n__f(X)))), c#(X) -> activate#(X))
     (f#(f(X)) -> c#(n__f(g(n__f(X)))), c#(X) -> d#(activate(X)))
     (c#(X) -> activate#(X), activate#(n__f(X)) -> f#(X))
     (c#(X) -> activate#(X), activate#(n__d(X)) -> d#(X))}
    SCCS:
     Scc:
      {             c#(X) -> activate#(X),
                 f#(f(X)) -> c#(n__f(g(n__f(X)))),
       activate#(n__f(X)) -> f#(X)}
     SCC:
      Strict:
       {             c#(X) -> activate#(X),
                  f#(f(X)) -> c#(n__f(g(n__f(X)))),
        activate#(n__f(X)) -> f#(X)}
      Weak:
      {             c(X) -> d(activate(X)),
                    f(X) -> n__f(X),
                 f(f(X)) -> c(n__f(g(n__f(X)))),
                    d(X) -> n__d(X),
             activate(X) -> X,
       activate(n__f(X)) -> f(X),
       activate(n__d(X)) -> d(X)}
      POLY:
       Argument Filtering:
        pi(n__d) = [], pi(activate#) = 0, pi(activate) = [], pi(d) = [], pi(f#) = 0, pi(f) = [], pi(g) = [], pi(n__f) = 0, pi(c#) = [0], pi(c) = []
       Usable Rules:
        {}
       Interpretation:
        [c#](x0) = x0 + 1,
        [f] = 1,
        [g] = 0
       Strict:
        {          f#(f(X)) -> c#(n__f(g(n__f(X)))),
         activate#(n__f(X)) -> f#(X)}
       Weak:
        {             c(X) -> d(activate(X)),
                      f(X) -> n__f(X),
                   f(f(X)) -> c(n__f(g(n__f(X)))),
                      d(X) -> n__d(X),
               activate(X) -> X,
         activate(n__f(X)) -> f(X),
         activate(n__d(X)) -> d(X)}
       EDG:
        {(activate#(n__f(X)) -> f#(X), f#(f(X)) -> c#(n__f(g(n__f(X)))))}
        SCCS:
         
         Qed