YES
Time: 0.000838
TRS:
 {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, a()),
    f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())),
    f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
  EDG:
   {(f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(a(), a()))
    (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(f(f(x, a()), f(a(), a())), a()))
    (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(f(x, a()), f(a(), a())))
    (f#(f(a(), x), a()) -> f#(x, a()), f#(f(a(), x), a()) -> f#(x, a()))}
   SCCS (1):
    Scc:
     {f#(f(a(), x), a()) -> f#(x, a())}
    SCC (1):
     Strict:
      {f#(f(a(), x), a()) -> f#(x, a())}
     Weak:
     {f(f(a(), x), a()) -> f(f(f(x, a()), f(a(), a())), a())}
     SPSC:
      Simple Projection:
       pi(f#) = 0
      Strict:
       {}
      Qed