YES
Time: 0.007296
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)))}
  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()))}
   SCCS (1):
    Scc:
     {f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x))}
    SCC (1):
     Strict:
      {f#(a(), f(x, a())) -> f#(a(), f(f(a(), a()), x))}
     Weak:
     {f(a(), f(x, a())) -> f(a(), f(a(), f(f(a(), a()), x)))}
     BOUND:
      Bound: match(-raise)-bounded by 1
      Automaton:
       {     a_1() -> 2*
             a_0() -> 1*
        f#_1(2, 4) -> 1*
        f#_0(1, 1) -> 1*
         f_1(3, 3) -> 4*
         f_1(3, 1) -> 4*
         f_1(2, 5) -> 5 | 1
         f_1(2, 4) -> 5*
         f_1(2, 2) -> 3*
         f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed