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)-bounded by 1
       Automaton:
        {   b_0() -> 5*
           f_1(9) -> 10*
           f_0(5) -> 6*
            a_0() -> 2*
         h#_1(10) -> 11*
          h#_0(6) -> 8*
          h_1(12) -> 13*
           h_0(6) -> 7*
           h_0(2) -> 3*
          g_1(13) -> 14*
           g_0(7) -> 4*
           g_0(3) -> 1*
               14 -> 7*
               11 -> 8*
               10 -> 12*
                3 -> 9*
                1 -> 6*}
       Strict:
        {}
       Qed