YES

Problem:
 f(n__f(n__a())) -> f(n__g(n__f(n__a())))
 f(X) -> n__f(X)
 a() -> n__a()
 g(X) -> n__g(X)
 activate(n__f(X)) -> f(X)
 activate(n__a()) -> a()
 activate(n__g(X)) -> g(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   f#(n__f(n__a())) -> f#(n__g(n__f(n__a())))
   activate#(n__f(X)) -> f#(X)
   activate#(n__a()) -> a#()
   activate#(n__g(X)) -> activate#(X)
   activate#(n__g(X)) -> g#(activate(X))
  TRS:
   f(n__f(n__a())) -> f(n__g(n__f(n__a())))
   f(X) -> n__f(X)
   a() -> n__a()
   g(X) -> n__g(X)
   activate(n__f(X)) -> f(X)
   activate(n__a()) -> a()
   activate(n__g(X)) -> g(activate(X))
   activate(X) -> X
  TDG Processor:
   DPs:
    f#(n__f(n__a())) -> f#(n__g(n__f(n__a())))
    activate#(n__f(X)) -> f#(X)
    activate#(n__a()) -> a#()
    activate#(n__g(X)) -> activate#(X)
    activate#(n__g(X)) -> g#(activate(X))
   TRS:
    f(n__f(n__a())) -> f(n__g(n__f(n__a())))
    f(X) -> n__f(X)
    a() -> n__a()
    g(X) -> n__g(X)
    activate(n__f(X)) -> f(X)
    activate(n__a()) -> a()
    activate(n__g(X)) -> g(activate(X))
    activate(X) -> X
   graph:
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__g(X)) -> g#(activate(X))
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__g(X)) -> activate#(X)
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__a()) -> a#()
    activate#(n__g(X)) -> activate#(X) -> activate#(n__f(X)) -> f#(X)
    activate#(n__f(X)) -> f#(X) ->
    f#(n__f(n__a())) -> f#(n__g(n__f(n__a())))
    f#(n__f(n__a())) -> f#(n__g(n__f(n__a()))) -> f#(n__f(n__a())) -> f#(n__g(n__f(n__a())))
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 6/25
    DPs:
     activate#(n__g(X)) -> activate#(X)
    TRS:
     f(n__f(n__a())) -> f(n__g(n__f(n__a())))
     f(X) -> n__f(X)
     a() -> n__a()
     g(X) -> n__g(X)
     activate(n__f(X)) -> f(X)
     activate(n__a()) -> a()
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(activate#) = 0
     problem:
      DPs:
       
      TRS:
       f(n__f(n__a())) -> f(n__g(n__f(n__a())))
       f(X) -> n__f(X)
       a() -> n__a()
       g(X) -> n__g(X)
       activate(n__f(X)) -> f(X)
       activate(n__a()) -> a()
       activate(n__g(X)) -> g(activate(X))
       activate(X) -> X
     Qed
    
    DPs:
     f#(n__f(n__a())) -> f#(n__g(n__f(n__a())))
    TRS:
     f(n__f(n__a())) -> f(n__g(n__f(n__a())))
     f(X) -> n__f(X)
     a() -> n__a()
     g(X) -> n__g(X)
     activate(n__f(X)) -> f(X)
     activate(n__a()) -> a()
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    EDG Processor:
     DPs:
      f#(n__f(n__a())) -> f#(n__g(n__f(n__a())))
     TRS:
      f(n__f(n__a())) -> f(n__g(n__f(n__a())))
      f(X) -> n__f(X)
      a() -> n__a()
      g(X) -> n__g(X)
      activate(n__f(X)) -> f(X)
      activate(n__a()) -> a()
      activate(n__g(X)) -> g(activate(X))
      activate(X) -> X
     graph:
      
     Qed