YES
Time: 0.003768
TRS:
 {f(x, f(a(), y)) -> f(f(y, f(f(a(), a()), a())), x)}
 DP:
  DP:
   {f#(x, f(a(), y)) -> f#(y, f(f(a(), a()), a())),
    f#(x, f(a(), y)) -> f#(f(y, f(f(a(), a()), a())), x),
    f#(x, f(a(), y)) -> f#(f(a(), a()), a()),
    f#(x, f(a(), y)) -> f#(a(), a())}
  TRS:
  {f(x, f(a(), y)) -> f(f(y, f(f(a(), a()), a())), x)}
  UR:
   {}
   EDG:
    {}
    STATUS:
     arrows: 1.000000
     SCCS (0):