YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a())) -> f#(g(n__f(n__a())))
   activate#(n__f(X)) -> activate#(X)
   activate#(n__f(X)) -> f#(activate(X))
   activate#(n__a()) -> a#()
  TRS:
   f(f(a())) -> f(g(n__f(n__a())))
   f(X) -> n__f(X)
   a() -> n__a()
   activate(n__f(X)) -> f(activate(X))
   activate(n__a()) -> a()
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    f(f(a())) -> f(g(n__f(n__a())))
    f(X) -> n__f(X)
    a() -> n__a()
    activate(n__f(X)) -> f(activate(X))
    activate(n__a()) -> a()
    activate(X) -> X
   interpretation:
    [activate#](x0) = 4x0 + 5,
    
    [a#] = 0,
    
    [f#](x0) = 4x0 + 2,
    
    [activate](x0) = 2x0 + 4,
    
    [g](x0) = 0,
    
    [n__f](x0) = 2x0 + 4,
    
    [n__a] = 1,
    
    [f](x0) = 2x0 + 4,
    
    [a] = 1
   orientation:
    f#(f(a())) = 26 >= 2 = f#(g(n__f(n__a())))
    
    activate#(n__f(X)) = 8X + 21 >= 4X + 5 = activate#(X)
    
    activate#(n__f(X)) = 8X + 21 >= 8X + 18 = f#(activate(X))
    
    activate#(n__a()) = 9 >= 0 = a#()
    
    f(f(a())) = 16 >= 4 = f(g(n__f(n__a())))
    
    f(X) = 2X + 4 >= 2X + 4 = n__f(X)
    
    a() = 1 >= 1 = n__a()
    
    activate(n__f(X)) = 4X + 12 >= 4X + 12 = f(activate(X))
    
    activate(n__a()) = 6 >= 1 = a()
    
    activate(X) = 2X + 4 >= X = X
   problem:
    DPs:
     
    TRS:
     f(f(a())) -> f(g(n__f(n__a())))
     f(X) -> n__f(X)
     a() -> n__a()
     activate(n__f(X)) -> f(activate(X))
     activate(n__a()) -> a()
     activate(X) -> X
   Qed