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-dp
     automaton:
      final states: {32,1}
      transitions:
       f1(22) -> 30*,20,23
       f1(19) -> 20*
       f1(31) -> 30,18,33*,20
       f80() -> 2*
       h{#,0}(33) -> 1*
       h{#,0}(18) -> 1*
       h{#,0}(3) -> 1*
       f0(17) -> 18*
       f0(2) -> 3*
       f0(31) -> 18*
       f0(8) -> 18*,3,9
       g0(17) -> 3*
       g0(7) -> 3*
       g0(31) -> 3*
       h0(6) -> 17,31*,22,19,8,7
       a0() -> 6*
       h{#,1}(30) -> 32*
       h{#,1}(20) -> 32*,1,21
       h{#,1}(33) -> 1,32*
       7 -> 22,8
       9 -> 3*
       17 -> 19*
       21 -> 1*
       23 -> 20*
     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