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