YES
TRS:
 {f(f(y, z), f(x, f(a(), x))) -> f(f(f(a(), z), f(x, a())), f(a(), y))}
 DP:
  Strict:
   {f#(f(y, z), f(x, f(a(), x))) -> f#(x, a()),
    f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)),
    f#(f(y, z), f(x, f(a(), x))) -> f#(f(a(), z), f(x, a())),
    f#(f(y, z), f(x, f(a(), x))) -> f#(a(), z),
    f#(f(y, z), f(x, f(a(), x))) -> f#(a(), y)}
  Weak:
  {f(f(y, z), f(x, f(a(), x))) -> f(f(f(a(), z), f(x, a())), f(a(), y))}
  EDG:
   {(f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)), f#(f(y, z), f(x, f(a(), x))) -> f#(a(), y))
    (f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)), f#(f(y, z), f(x, f(a(), x))) -> f#(a(), z))
    (f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)), f#(f(y, z), f(x, f(a(), x))) -> f#(f(a(), z), f(x, a())))
    (f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)), f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)))
    (f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y)), f#(f(y, z), f(x, f(a(), x))) -> f#(x, a()))}
   SCCS:
    Scc:
     {f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y))}
    SCC:
     Strict:
      {f#(f(y, z), f(x, f(a(), x))) -> f#(f(f(a(), z), f(x, a())), f(a(), y))}
     Weak:
     {f(f(y, z), f(x, f(a(), x))) -> f(f(f(a(), z), f(x, a())), f(a(), y))}
     BOUND:
      Bound: match(-raise)-bounded by 1
      Automaton:
       {       b_0() -> 3*
               a_1() -> 15* | 10 | 2
               a_0() -> 2*
        f#_1(19, 17) -> 8*
        f#_1(19, 14) -> 8*
        f#_1(13, 17) -> 8*
        f#_1(13, 14) -> 8*
        f#_0(19, 18) -> 8*
        f#_0(19, 17) -> 8*
         f#_0(19, 9) -> 8*
         f#_0(19, 7) -> 8*
         f#_0(19, 4) -> 8*
         f#_0(6, 18) -> 8*
         f#_0(6, 17) -> 8*
          f#_0(6, 9) -> 8*
          f#_0(6, 7) -> 8*
          f#_0(6, 4) -> 8*
         f_1(18, 16) -> 19* | 13 | 6
         f_1(18, 12) -> 13*
         f_1(15, 18) -> 17* | 14 | 7
         f_1(15, 16) -> 18* | 11 | 4
         f_1(15, 15) -> 16* | 12 | 5
         f_1(15, 10) -> 12*
          f_1(15, 9) -> 17* | 14 | 7
          f_1(15, 5) -> 18* | 11 | 4
          f_1(15, 4) -> 17* | 14 | 7
         f_1(11, 16) -> 13*
         f_1(11, 12) -> 13*
         f_1(10, 18) -> 14*
         f_1(10, 16) -> 11*
          f_1(10, 9) -> 14*
          f_1(10, 5) -> 11*
          f_1(10, 4) -> 14*
          f_1(2, 15) -> 16* | 12 | 5
          f_1(2, 10) -> 12*
         f_0(19, 17) -> 1*
          f_0(19, 9) -> 1*
          f_0(19, 7) -> 1*
         f_0(18, 16) -> 6*
          f_0(18, 5) -> 6*
         f_0(16, 15) -> 5*
          f_0(16, 2) -> 5*
         f_0(15, 18) -> 7*
         f_0(15, 16) -> 4*
         f_0(15, 15) -> 5*
          f_0(15, 9) -> 7*
          f_0(15, 5) -> 4*
          f_0(15, 4) -> 7*
          f_0(15, 3) -> 9*
          f_0(15, 2) -> 5*
          f_0(9, 16) -> 6*
           f_0(9, 5) -> 6*
          f_0(6, 17) -> 1*
           f_0(6, 9) -> 1*
           f_0(6, 7) -> 1*
          f_0(5, 15) -> 5*
           f_0(5, 2) -> 5*
          f_0(4, 16) -> 6*
           f_0(4, 5) -> 6*
          f_0(3, 15) -> 5*
           f_0(3, 2) -> 5*
          f_0(2, 18) -> 7*
          f_0(2, 16) -> 4*
          f_0(2, 15) -> 5*
           f_0(2, 9) -> 7*
           f_0(2, 5) -> 4*
           f_0(2, 4) -> 7*
           f_0(2, 3) -> 9*
           f_0(2, 2) -> 5*}
      Strict:
       {}
      Qed