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