YES
Time: 0.000826
TRS:
 {  g(x, y) -> h(x, y),
  h(f x, y) -> f g(x, y)}
 DP:
  DP:
   {  g#(x, y) -> h#(x, y),
    h#(f x, y) -> g#(x, y)}
  TRS:
  {  g(x, y) -> h(x, y),
   h(f x, y) -> f g(x, y)}
  EDG:
   {(h#(f x, y) -> g#(x, y), g#(x, y) -> h#(x, y))
    (g#(x, y) -> h#(x, y), h#(f x, y) -> g#(x, y))}
   SCCS (1):
    Scc:
     {  g#(x, y) -> h#(x, y),
      h#(f x, y) -> g#(x, y)}
    SCC (2):
     Strict:
      {  g#(x, y) -> h#(x, y),
       h#(f x, y) -> g#(x, y)}
     Weak:
     {  g(x, y) -> h(x, y),
      h(f x, y) -> f g(x, y)}
     SPSC:
      Simple Projection:
       pi(h#) = 0, pi(g#) = 0
      Strict:
       {g#(x, y) -> h#(x, y)}
      EDG:
       {}
       SCCS (0):
        
        Qed