YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a())) -> f#(g(n__f(a())))
   activate#(n__f(X)) -> f#(X)
  TRS:
   f(f(a())) -> f(g(n__f(a())))
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    f#(f(a())) -> f#(g(n__f(a())))
    activate#(n__f(X)) -> f#(X)
   TRS:
    
   ADG Processor:
    DPs:
     f#(f(a())) -> f#(g(n__f(a())))
     activate#(n__f(X)) -> f#(X)
    TRS:
     
    graph:
     activate#(n__f(X)) -> f#(X) -> f#(f(a())) -> f#(g(n__f(a())))
    Restore Modifier:
     DPs:
      f#(f(a())) -> f#(g(n__f(a())))
      activate#(n__f(X)) -> f#(X)
     TRS:
      f(f(a())) -> f(g(n__f(a())))
      f(X) -> n__f(X)
      activate(n__f(X)) -> f(X)
      activate(X) -> X
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/4