YES
TRS:
 {f(a(), x) -> f(g(x), x),
    g(h(x)) -> g(x),
    h(g(x)) -> h(a()),
    h(h(x)) -> x}
 DP:
  Strict:
   {f#(a(), x) -> f#(g(x), x),
    f#(a(), x) -> g#(x),
      g#(h(x)) -> g#(x),
      h#(g(x)) -> h#(a())}
  Weak:
  {f(a(), x) -> f(g(x), x),
     g(h(x)) -> g(x),
     h(g(x)) -> h(a()),
     h(h(x)) -> x}
  EDG:
   {(f#(a(), x) -> g#(x), g#(h(x)) -> g#(x))
    (f#(a(), x) -> f#(g(x), x), f#(a(), x) -> g#(x))
    (f#(a(), x) -> f#(g(x), x), f#(a(), x) -> f#(g(x), x))
    (g#(h(x)) -> g#(x), g#(h(x)) -> g#(x))}
   SCCS:
    Scc:
     {g#(h(x)) -> g#(x)}
    Scc:
     {f#(a(), x) -> f#(g(x), x)}
    SCC:
     Strict:
      {g#(h(x)) -> g#(x)}
     Weak:
     {f(a(), x) -> f(g(x), x),
        g(h(x)) -> g(x),
        h(g(x)) -> h(a()),
        h(h(x)) -> x}
     SPSC:
      Simple Projection:
       pi(g#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {f#(a(), x) -> f#(g(x), x)}
     Weak:
     {f(a(), x) -> f(g(x), x),
        g(h(x)) -> g(x),
        h(g(x)) -> h(a()),
        h(h(x)) -> x}
     POLY:
      Argument Filtering:
       pi(h) = [], pi(a) = [], pi(g) = [], pi(f#) = 0, pi(f) = []
      Usable Rules:
       {}
      Interpretation:
       [g] = 0,
       [a] = 1
      Strict:
       {}
      Weak:
       {f(a(), x) -> f(g(x), x),
          g(h(x)) -> g(x),
          h(g(x)) -> h(a()),
          h(h(x)) -> x}
      Qed