YES
Time: 0.000686
TRS:
 {f(f(a(), f(x, a())), a()) -> f(a(), f(f(x, a()), a()))}
 DP:
  DP:
   {f#(f(a(), f(x, a())), a()) -> f#(f(x, a()), a()),
    f#(f(a(), f(x, a())), a()) -> f#(a(), f(f(x, a()), a()))}
  TRS:
  {f(f(a(), f(x, a())), a()) -> f(a(), f(f(x, a()), a()))}
  EDG:
   {(f#(f(a(), f(x, a())), a()) -> f#(f(x, a()), a()), f#(f(a(), f(x, a())), a()) -> f#(a(), f(f(x, a()), a())))
    (f#(f(a(), f(x, a())), a()) -> f#(f(x, a()), a()), f#(f(a(), f(x, a())), a()) -> f#(f(x, a()), a()))}
   SCCS (1):
    Scc:
     {f#(f(a(), f(x, a())), a()) -> f#(f(x, a()), a())}
    SCC (1):
     Strict:
      {f#(f(a(), f(x, a())), a()) -> f#(f(x, a()), a())}
     Weak:
     {f(f(a(), f(x, a())), a()) -> f(a(), f(f(x, a()), a()))}
     SPSC:
      Simple Projection:
       pi(f#) = 0
      Strict:
       {}
      Qed