YES
Time: 0.002796
TRS:
 {f(a(), f(x, a())) -> f(a(), f(a(), f(f(a(), a()), x)))}
 DP:
  DP:
   {f#(a(), f(x, a())) -> f#(f(a(), a()), x),
    f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)),
    f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))),
    f#(a(), f(x, a())) -> f#(a(), a())}
  TRS:
  {f(a(), f(x, a())) -> f(a(), f(a(), f(f(a(), a()), x)))}
  UR:
   {f(a(), f(x, a())) -> f(a(), f(a(), f(f(a(), a()), x)))}
   EDG:
    {(f#(a(), f(x, a())) -> f#(f(a(), a()), x), f#(a(), f(x, a())) -> f#(a(), a()))
     (f#(a(), f(x, a())) -> f#(f(a(), a()), x), f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))))
     (f#(a(), f(x, a())) -> f#(f(a(), a()), x), f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)))
     (f#(a(), f(x, a())) -> f#(f(a(), a()), x), f#(a(), f(x, a())) -> f#(f(a(), a()), x))
     (f#(a(), f(x, a())) -> f#(a(), a()), f#(a(), f(x, a())) -> f#(a(), a()))
     (f#(a(), f(x, a())) -> f#(a(), a()), f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))))
     (f#(a(), f(x, a())) -> f#(a(), a()), f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)))
     (f#(a(), f(x, a())) -> f#(a(), a()), f#(a(), f(x, a())) -> f#(f(a(), a()), x))
     (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(f(a(), a()), x))
     (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)))
     (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))))
     (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(a(), a()))
     (f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))), f#(a(), f(x, a())) -> f#(f(a(), a()), x))
     (f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))), f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)))
     (f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))), f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))))
     (f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))), f#(a(), f(x, a())) -> f#(a(), a()))}
    EDG:
     {(f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(f(a(), a()), x))
      (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)))
      (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(a(), f(a(), f(f(a(), a()), x))))
      (f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x)), f#(a(), f(x, a())) -> f#(a(), a()))}
     EDG:
      {}
      EDG:
       {}
       STATUS:
        arrows: 1.000000
        SCCS (0):