YES
Time: 0.003498
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:
   {}
   STATUS:
    arrows: 1.000000
    SCCS (0):