YES

Problem:
 f(a()) -> g(h(a()))
 h(g(x)) -> g(h(f(x)))
 k(x,h(x),a()) -> h(x)
 k(f(x),y,x) -> f(x)

Proof:
 DP Processor:
  DPs:
   f#(a()) -> h#(a())
   h#(g(x)) -> f#(x)
   h#(g(x)) -> h#(f(x))
  TRS:
   f(a()) -> g(h(a()))
   h(g(x)) -> g(h(f(x)))
   k(x,h(x),a()) -> h(x)
   k(f(x),y,x) -> f(x)
  EDG Processor:
   DPs:
    f#(a()) -> h#(a())
    h#(g(x)) -> f#(x)
    h#(g(x)) -> h#(f(x))
   TRS:
    f(a()) -> g(h(a()))
    h(g(x)) -> g(h(f(x)))
    k(x,h(x),a()) -> h(x)
    k(f(x),y,x) -> f(x)
   graph:
    h#(g(x)) -> h#(f(x)) -> h#(g(x)) -> f#(x)
    h#(g(x)) -> h#(f(x)) -> h#(g(x)) -> h#(f(x))
    h#(g(x)) -> f#(x) -> f#(a()) -> h#(a())
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     h#(g(x)) -> h#(f(x))
    TRS:
     f(a()) -> g(h(a()))
     h(g(x)) -> g(h(f(x)))
     k(x,h(x),a()) -> h(x)
     k(f(x),y,x) -> f(x)
    Usable Rule Processor:
     DPs:
      h#(g(x)) -> h#(f(x))
     TRS:
      f(a()) -> g(h(a()))
     Bounds Processor:
      bound: 2
      enrichment: match-dp
      automaton:
       final states: {6}
       transitions:
        h{#,0}(7) -> 6*
        g0(2) -> 2*
        g0(4) -> 2*
        g0(1) -> 2*
        g0(3) -> 2*
        f0(5) -> 7*
        f0(2) -> 1*
        f0(4) -> 1*
        f0(1) -> 1*
        f0(3) -> 1*
        a0() -> 3*
        h0(2) -> 4*
        h0(4) -> 4*
        h0(1) -> 4*
        h0(3) -> 4*
        h{#,1}(12) -> 13*
        f1(20) -> 21*
        f1(22) -> 23*
        f1(14) -> 15*
        f1(11) -> 12*
        g1(30) -> 31*
        h1(29) -> 30*
        a1() -> 29*
        h{#,2}(33) -> 34*
        f2(32) -> 33*
        1 -> 20,5
        2 -> 11,7,1,5
        3 -> 22,5
        4 -> 14,5
        13 -> 6*
        15 -> 12*
        21 -> 12*
        23 -> 12*
        30 -> 32*
        31 -> 23,12
        34 -> 13,6
      problem:
       DPs:
        
       TRS:
        f(a()) -> g(h(a()))
      Qed