YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(),h(x)) -> g#(x)
   f#(a(),h(x)) -> f#(g(x),h(x))
   h#(g(x)) -> h#(a())
   g#(h(x)) -> g#(x)
  TRS:
   f(a(),h(x)) -> f(g(x),h(x))
   h(g(x)) -> h(a())
   g(h(x)) -> g(x)
   h(h(x)) -> x
  TDG Processor:
   DPs:
    f#(a(),h(x)) -> g#(x)
    f#(a(),h(x)) -> f#(g(x),h(x))
    h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x)
   TRS:
    f(a(),h(x)) -> f(g(x),h(x))
    h(g(x)) -> h(a())
    g(h(x)) -> g(x)
    h(h(x)) -> x
   graph:
    h#(g(x)) -> h#(a()) -> h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
    f#(a(),h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
    f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> f#(g(x),h(x))
    f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> g#(x)
   EDG Processor:
    DPs:
     f#(a(),h(x)) -> g#(x)
     f#(a(),h(x)) -> f#(g(x),h(x))
     h#(g(x)) -> h#(a())
     g#(h(x)) -> g#(x)
    TRS:
     f(a(),h(x)) -> f(g(x),h(x))
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    graph:
     g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
     f#(a(),h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
     f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> g#(x)
     f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> f#(g(x),h(x))
    CDG Processor:
     DPs:
      f#(a(),h(x)) -> g#(x)
      f#(a(),h(x)) -> f#(g(x),h(x))
      h#(g(x)) -> h#(a())
      g#(h(x)) -> g#(x)
     TRS:
      f(a(),h(x)) -> f(g(x),h(x))
      h(g(x)) -> h(a())
      g(h(x)) -> g(x)
      h(h(x)) -> x
     graph:
      g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
      f#(a(),h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/16
      DPs:
       g#(h(x)) -> g#(x)
      TRS:
       f(a(),h(x)) -> f(g(x),h(x))
       h(g(x)) -> h(a())
       g(h(x)) -> g(x)
       h(h(x)) -> x
      KBO Processor:
       argument filtering:
        pi(a) = []
        pi(h) = [0]
        pi(f) = 1
        pi(g) = []
        pi(g#) = 0
       weight function:
        w0 = 1
        w(g#) = w(g) = w(f) = w(h) = w(a) = 1
       precedence:
        g# ~ g ~ h > f ~ a
       problem:
        DPs:
         
        TRS:
         f(a(),h(x)) -> f(g(x),h(x))
         h(g(x)) -> h(a())
         g(h(x)) -> g(x)
         h(h(x)) -> x
       Qed