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