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)
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {16,13,12,3,9,7,4,1}
      transitions:
       f80() -> 2*
       h{#,0}(12) -> 1*
       h{#,0}(16) -> 1*
       h{#,0}(3) -> 1*
       f0(2) -> 3*
       g0(17) -> 13*
       g0(6) -> 12*,3,4
       g0(13) -> 13*
       g0(8) -> 13*,9,8,7
       h0(5) -> 6*
       h0(12) -> 8*
       h0(2) -> 9*
       h0(16) -> 8*
       h0(3) -> 8*
       a0() -> 5*
       g1(15) -> 8*
       g1(17) -> 13*,8
       h1(14) -> 15*
       h1(16) -> 17*,8,15
       f1(6) -> 16*,3,14
       h{#,1}(14) -> 1*
       h{#,1}(16) -> 1*
       4 -> 3*
       7 -> 9*
     problem:
      DPs:
       
      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)
     Qed