YES

Problem:
 f(f(X)) -> c(n__f(g(n__f(X))))
 c(X) -> d(activate(X))
 h(X) -> c(n__d(X))
 f(X) -> n__f(X)
 d(X) -> n__d(X)
 activate(n__f(X)) -> f(X)
 activate(n__d(X)) -> d(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(f(X)) -> c#(n__f(g(n__f(X))))
   c#(X) -> activate#(X)
   c#(X) -> d#(activate(X))
   h#(X) -> c#(n__d(X))
   activate#(n__f(X)) -> f#(X)
   activate#(n__d(X)) -> d#(X)
  TRS:
   f(f(X)) -> c(n__f(g(n__f(X))))
   c(X) -> d(activate(X))
   h(X) -> c(n__d(X))
   f(X) -> n__f(X)
   d(X) -> n__d(X)
   activate(n__f(X)) -> f(X)
   activate(n__d(X)) -> d(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(f(X)) -> c#(n__f(g(n__f(X))))
    c#(X) -> activate#(X)
    c#(X) -> d#(activate(X))
    h#(X) -> c#(n__d(X))
    activate#(n__f(X)) -> f#(X)
    activate#(n__d(X)) -> d#(X)
   TRS:
    f(f(X)) -> c(n__f(g(n__f(X))))
    c(X) -> d(activate(X))
    h(X) -> c(n__d(X))
    f(X) -> n__f(X)
    d(X) -> n__d(X)
    activate(n__f(X)) -> f(X)
    activate(n__d(X)) -> d(X)
    activate(X) -> X
   graph:
    h#(X) -> c#(n__d(X)) -> c#(X) -> d#(activate(X))
    h#(X) -> c#(n__d(X)) -> c#(X) -> activate#(X)
    activate#(n__f(X)) -> f#(X) -> f#(f(X)) -> c#(n__f(g(n__f(X))))
    c#(X) -> activate#(X) -> activate#(n__d(X)) -> d#(X)
    c#(X) -> activate#(X) -> activate#(n__f(X)) -> f#(X)
    f#(f(X)) -> c#(n__f(g(n__f(X)))) -> c#(X) -> d#(activate(X))
    f#(f(X)) -> c#(n__f(g(n__f(X)))) -> c#(X) -> activate#(X)
   CDG Processor:
    DPs:
     f#(f(X)) -> c#(n__f(g(n__f(X))))
     c#(X) -> activate#(X)
     c#(X) -> d#(activate(X))
     h#(X) -> c#(n__d(X))
     activate#(n__f(X)) -> f#(X)
     activate#(n__d(X)) -> d#(X)
    TRS:
     f(f(X)) -> c(n__f(g(n__f(X))))
     c(X) -> d(activate(X))
     h(X) -> c(n__d(X))
     f(X) -> n__f(X)
     d(X) -> n__d(X)
     activate(n__f(X)) -> f(X)
     activate(n__d(X)) -> d(X)
     activate(X) -> X
    graph:
     h#(X) -> c#(n__d(X)) -> c#(X) -> activate#(X)
     h#(X) -> c#(n__d(X)) -> c#(X) -> d#(activate(X))
     c#(X) -> activate#(X) -> activate#(n__f(X)) -> 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))
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 5/36