YES
TRS:
 {        h(g(x)) -> g(h(f(x))),
           f(a()) -> g(h(a())),
  k(x, h(x), a()) -> h(x),
    k(f(x), y, x) -> f(x)}
 RUF:
  Strict:
   {h(g(x)) -> g(h(f(x))),
     f(a()) -> g(h(a()))}
  Weak:
   {}
  DP:
   Strict:
    {h#(g(x)) -> h#(f(x)),
     h#(g(x)) -> f#(x),
      f#(a()) -> h#(a())}
   Weak:
   {h(g(x)) -> g(h(f(x))),
     f(a()) -> g(h(a()))}
   EDG:
    {(h#(g(x)) -> f#(x), f#(a()) -> h#(a()))
     (h#(g(x)) -> h#(f(x)), h#(g(x)) -> h#(f(x)))
     (h#(g(x)) -> h#(f(x)), h#(g(x)) -> f#(x))}
    SCCS:
     Scc:
      {h#(g(x)) -> h#(f(x))}
     SCC:
      Strict:
       {h#(g(x)) -> h#(f(x))}
      Weak:
      {h(g(x)) -> g(h(f(x))),
        f(a()) -> g(h(a()))}
      BOUND:
       Bound: match(-raise)-DP-bounded by 2
       Automaton:
        { f_2(25) -> 26*
          f_1(20) -> 21*
          f_1(18) -> 19*
          f_1(16) -> 17*
          f_1(13) -> 14*
          f_0(12) -> 12*
          f_0(11) -> 12*
           f_0(9) -> 12*
           f_0(8) -> 12*
            a_1() -> 22*
            a_0() -> 11*
         h#_2(26) -> 27*
         h#_1(14) -> 15*
         h#_0(12) -> 6*
          h_1(22) -> 23*
          h_0(12) -> 9*
          h_0(11) -> 9*
           h_0(9) -> 9*
           h_0(8) -> 9*
          g_1(23) -> 24*
          g_0(12) -> 8*
          g_0(11) -> 8*
           g_0(9) -> 8*
           g_0(8) -> 8*
               27 -> 15*
               24 -> 19*
               23 -> 25*
               21 -> 14*
               19 -> 14*
               17 -> 14*
               15 -> 6*
               12 -> 20*
               11 -> 18*
                9 -> 16*
                8 -> 13 | 12 | 9}
       Strict:
        {}
       Qed