YES
Time: 0.002762
TRS:
 {f(f(a(), x), a()) -> f(f(x, f(a(), f(a(), a()))), a())}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, f(a(), f(a(), a()))),
    f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()),
    f#(f(a(), x), a()) -> f#(a(), f(a(), a())),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(x, f(a(), f(a(), a()))), a())}
  EDG:
   {(f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(x, f(a(), f(a(), a()))))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(a(), f(a(), a())))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(a(), a()))}
   EDG:
    {}
    EDG:
     {}
     STATUS:
      arrows: 1.000000
      SCCS (0):