YES
Time: 0.000827
TRS:
 {f(a(), f(x, a())) -> f(a(), f(f(a(), a()), f(a(), x)))}
 DP:
  DP:
   {f#(a(), f(x, a())) -> f#(f(a(), a()), f(a(), x)),
    f#(a(), f(x, a())) -> f#(a(), x),
    f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), f(a(), x))),
    f#(a(), f(x, a())) -> f#(a(), a())}
  TRS:
  {f(a(), f(x, a())) -> f(a(), f(f(a(), a()), f(a(), x)))}
  EDG:
   {(f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(f(a(), a()), f(a(), x)))
    (f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(a(), x))
    (f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), f(a(), x))))
    (f#(a(), f(x, a())) -> f#(a(), x), f#(a(), f(x, a())) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(a(), f(x, a())) -> f#(a(), x)}
    SCC (1):
     Strict:
      {f#(a(), f(x, a())) -> f#(a(), x)}
     Weak:
     {f(a(), f(x, a())) -> f(a(), f(f(a(), a()), f(a(), x)))}
     SPSC:
      Simple Projection:
       pi(f#) = 1
      Strict:
       {}
      Qed