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