YES
TRS:
 {             f(X) -> n__f(X),
          f(f(a())) -> c(n__f(n__g(n__f(n__a())))),
                a() -> n__a(),
               g(X) -> n__g(X),
        activate(X) -> X,
  activate(n__f(X)) -> f(activate(X)),
  activate(n__g(X)) -> g(activate(X)),
   activate(n__a()) -> a()}
 DP:
  Strict:
   {activate#(n__f(X)) -> f#(activate(X)),
    activate#(n__f(X)) -> activate#(X),
    activate#(n__g(X)) -> g#(activate(X)),
    activate#(n__g(X)) -> activate#(X),
     activate#(n__a()) -> a#()}
  Weak:
  {             f(X) -> n__f(X),
           f(f(a())) -> c(n__f(n__g(n__f(n__a())))),
                 a() -> n__a(),
                g(X) -> n__g(X),
         activate(X) -> X,
   activate(n__f(X)) -> f(activate(X)),
   activate(n__g(X)) -> g(activate(X)),
    activate(n__a()) -> a()}
  EDG:
   {(activate#(n__g(X)) -> activate#(X), activate#(n__a()) -> a#())
    (activate#(n__g(X)) -> activate#(X), activate#(n__g(X)) -> activate#(X))
    (activate#(n__g(X)) -> activate#(X), activate#(n__g(X)) -> g#(activate(X)))
    (activate#(n__g(X)) -> activate#(X), activate#(n__f(X)) -> activate#(X))
    (activate#(n__g(X)) -> activate#(X), activate#(n__f(X)) -> f#(activate(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)) -> activate#(X), activate#(n__g(X)) -> g#(activate(X)))
    (activate#(n__f(X)) -> activate#(X), activate#(n__g(X)) -> activate#(X))
    (activate#(n__f(X)) -> activate#(X), activate#(n__a()) -> a#())}
   SCCS:
    Scc:
     {activate#(n__f(X)) -> activate#(X),
      activate#(n__g(X)) -> activate#(X)}
    SCC:
     Strict:
      {activate#(n__f(X)) -> activate#(X),
       activate#(n__g(X)) -> activate#(X)}
     Weak:
     {             f(X) -> n__f(X),
              f(f(a())) -> c(n__f(n__g(n__f(n__a())))),
                    a() -> n__a(),
                   g(X) -> n__g(X),
            activate(X) -> X,
      activate(n__f(X)) -> f(activate(X)),
      activate(n__g(X)) -> g(activate(X)),
       activate(n__a()) -> a()}
     SPSC:
      Simple Projection:
       pi(activate#) = 0
      Strict:
       {activate#(n__g(X)) -> activate#(X)}
      EDG:
       {(activate#(n__g(X)) -> activate#(X), activate#(n__g(X)) -> activate#(X))}
       SCCS:
        Scc:
         {activate#(n__g(X)) -> activate#(X)}
        SCC:
         Strict:
          {activate#(n__g(X)) -> activate#(X)}
         Weak:
         {             f(X) -> n__f(X),
                  f(f(a())) -> c(n__f(n__g(n__f(n__a())))),
                        a() -> n__a(),
                       g(X) -> n__g(X),
                activate(X) -> X,
          activate(n__f(X)) -> f(activate(X)),
          activate(n__g(X)) -> g(activate(X)),
           activate(n__a()) -> a()}
         SPSC:
          Simple Projection:
           pi(activate#) = 0
          Strict:
           {}
          Qed