YES
TRS:
 {g(g(x)) -> f(x),
  f(f(x)) -> g(f(x))}
 DP:
  Strict:
   {g#(g(x)) -> f#(x),
    f#(f(x)) -> g#(f(x))}
  Weak:
  {g(g(x)) -> f(x),
   f(f(x)) -> g(f(x))}
  EDG:
   {(f#(f(x)) -> g#(f(x)), g#(g(x)) -> f#(x))
    (g#(g(x)) -> f#(x), f#(f(x)) -> g#(f(x)))}
   SCCS:
    Scc:
     {g#(g(x)) -> f#(x),
      f#(f(x)) -> g#(f(x))}
    SCC:
     Strict:
      {g#(g(x)) -> f#(x),
       f#(f(x)) -> g#(f(x))}
     Weak:
     {g(g(x)) -> f(x),
      f(f(x)) -> g(f(x))}
     SPSC:
      Simple Projection:
       pi(f#) = 0, pi(g#) = 0
      Strict:
       {f#(f(x)) -> g#(f(x))}
      EDG:
       {}
       SCCS:
        
        Qed