YES
Time: 0.000764
TRS:
 {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
 DP:
  DP:
   {f#(g(x, y), f(y, y)) -> f#(g(y, x), y)}
  TRS:
  {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
  EDG:
   {(f#(g(x, y), f(y, y)) -> f#(g(y, x), y), f#(g(x, y), f(y, y)) -> f#(g(y, x), y))}
   SCCS (1):
    Scc:
     {f#(g(x, y), f(y, y)) -> f#(g(y, x), y)}
    SCC (1):
     Strict:
      {f#(g(x, y), f(y, y)) -> f#(g(y, x), y)}
     Weak:
     {f(g(x, y), f(y, y)) -> f(g(y, x), y)}
     SPSC:
      Simple Projection:
       pi(f#) = 1
      Strict:
       {}
      Qed