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