YES
TRS:
 {f(f(x)) -> f(g(f(x), x)),
  f(f(x)) -> f(h(f(x), f(x))),
  g(x, y) -> y,
  h(x, x) -> g(x, 0())}
 DP:
  Strict:
   {f#(f(x)) -> f#(g(f(x), x)),
    f#(f(x)) -> f#(h(f(x), f(x))),
    f#(f(x)) -> g#(f(x), x),
    f#(f(x)) -> h#(f(x), f(x)),
    h#(x, x) -> g#(x, 0())}
  Weak:
  {f(f(x)) -> f(g(f(x), x)),
   f(f(x)) -> f(h(f(x), f(x))),
   g(x, y) -> y,
   h(x, x) -> g(x, 0())}
  EDG:
   {(f#(f(x)) -> f#(g(f(x), x)), f#(f(x)) -> h#(f(x), f(x)))
    (f#(f(x)) -> f#(g(f(x), x)), f#(f(x)) -> g#(f(x), x))
    (f#(f(x)) -> f#(g(f(x), x)), f#(f(x)) -> f#(h(f(x), f(x))))
    (f#(f(x)) -> f#(g(f(x), x)), f#(f(x)) -> f#(g(f(x), x)))
    (f#(f(x)) -> h#(f(x), f(x)), h#(x, x) -> g#(x, 0()))
    (f#(f(x)) -> f#(h(f(x), f(x))), f#(f(x)) -> f#(g(f(x), x)))
    (f#(f(x)) -> f#(h(f(x), f(x))), f#(f(x)) -> f#(h(f(x), f(x))))
    (f#(f(x)) -> f#(h(f(x), f(x))), f#(f(x)) -> g#(f(x), x))
    (f#(f(x)) -> f#(h(f(x), f(x))), f#(f(x)) -> h#(f(x), f(x)))}
   SCCS:
    Scc:
     {f#(f(x)) -> f#(g(f(x), x)),
      f#(f(x)) -> f#(h(f(x), f(x)))}
    SCC:
     Strict:
      {f#(f(x)) -> f#(g(f(x), x)),
       f#(f(x)) -> f#(h(f(x), f(x)))}
     Weak:
     {f(f(x)) -> f(g(f(x), x)),
      f(f(x)) -> f(h(f(x), f(x))),
      g(x, y) -> y,
      h(x, x) -> g(x, 0())}
     POLY:
      Argument Filtering:
       pi(0) = [], pi(h) = [], pi(g) = 1, pi(f#) = 0, pi(f) = [0]
      Usable Rules:
       {}
      Interpretation:
       [h] = 0,
       [f](x0) = x0 + 1
      Strict:
       {}
      Weak:
       {f(f(x)) -> f(g(f(x), x)),
        f(f(x)) -> f(h(f(x), f(x))),
        g(x, y) -> y,
        h(x, x) -> g(x, 0())}
      Qed