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
      automaton:
       final states: {7}
       transitions:
        f0(6) -> 6*
        a0() -> 6*
        h0(6) -> 6*
        g1(15) -> 16*
        h1(14) -> 15*
        a1() -> 14*
        h{#,1}(12) -> 13*
        f1(21) -> 22*
        f1(11) -> 12*
        h{#,2}(29) -> 30*
        h{#,0}(6) -> 7*
        f2(28) -> 29*
        g0(6) -> 6*
        6 -> 11*
        13 -> 7*
        15 -> 28,21
        16 -> 12,6
        22 -> 12*
        30 -> 13,7
      problem:
       DPs:
        
       TRS:
        f(a()) -> g(h(a()))
      Qed