MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(f(X)) -> c#(n__f(n__g(n__f(X))))
   c#(X) -> activate#(X)
   c#(X) -> d#(activate(X))
   h#(X) -> c#(n__d(X))
   activate#(n__f(X)) -> activate#(X)
   activate#(n__f(X)) -> f#(activate(X))
   activate#(n__g(X)) -> g#(X)
   activate#(n__d(X)) -> d#(X)
  TRS:
   f(f(X)) -> c(n__f(n__g(n__f(X))))
   c(X) -> d(activate(X))
   h(X) -> c(n__d(X))
   f(X) -> n__f(X)
   g(X) -> n__g(X)
   d(X) -> n__d(X)
   activate(n__f(X)) -> f(activate(X))
   activate(n__g(X)) -> g(X)
   activate(n__d(X)) -> d(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(f(X)) -> c#(n__f(n__g(n__f(X))))
    c#(X) -> activate#(X)
    c#(X) -> d#(activate(X))
    h#(X) -> c#(n__d(X))
    activate#(n__f(X)) -> activate#(X)
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__g(X)) -> g#(X)
    activate#(n__d(X)) -> d#(X)
   TRS:
    f(f(X)) -> c(n__f(n__g(n__f(X))))
    c(X) -> d(activate(X))
    h(X) -> c(n__d(X))
    f(X) -> n__f(X)
    g(X) -> n__g(X)
    d(X) -> n__d(X)
    activate(n__f(X)) -> f(activate(X))
    activate(n__g(X)) -> g(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)) -> activate#(X) ->
    activate#(n__d(X)) -> d#(X)
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__g(X)) -> g#(X)
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__f(X)) -> activate#(X)
    activate#(n__f(X)) -> f#(activate(X)) ->
    f#(f(X)) -> c#(n__f(n__g(n__f(X))))
    c#(X) -> activate#(X) -> activate#(n__d(X)) -> d#(X)
    c#(X) -> activate#(X) -> activate#(n__g(X)) -> g#(X)
    c#(X) -> activate#(X) -> activate#(n__f(X)) -> f#(activate(X))
    c#(X) -> activate#(X) -> activate#(n__f(X)) -> activate#(X)
    f#(f(X)) -> c#(n__f(n__g(n__f(X)))) ->
    c#(X) -> d#(activate(X))
    f#(f(X)) -> c#(n__f(n__g(n__f(X)))) -> c#(X) -> activate#(X)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 13/64
    DPs:
     c#(X) -> activate#(X)
     activate#(n__f(X)) -> activate#(X)
     activate#(n__f(X)) -> f#(activate(X))
     f#(f(X)) -> c#(n__f(n__g(n__f(X))))
    TRS:
     f(f(X)) -> c(n__f(n__g(n__f(X))))
     c(X) -> d(activate(X))
     h(X) -> c(n__d(X))
     f(X) -> n__f(X)
     g(X) -> n__g(X)
     d(X) -> n__d(X)
     activate(n__f(X)) -> f(activate(X))
     activate(n__g(X)) -> g(X)
     activate(n__d(X)) -> d(X)
     activate(X) -> X
    Open