YES
Time: 0.000612
TRS:
 {f(X, g X) -> f(1(), g X),
      g 1() -> g 0()}
 DP:
  DP:
   {f#(X, g X) -> f#(1(), g X),
        g# 1() -> g# 0()}
  TRS:
  {f(X, g X) -> f(1(), g X),
       g 1() -> g 0()}
  EDG:
   {(g# 1() -> g# 0(), g# 1() -> g# 0())
    (f#(X, g X) -> f#(1(), g X), f#(X, g X) -> f#(1(), g X))}
   EDG:
    {}
    EDG:
     {}
     EDG:
      {}
      STATUS:
       arrows: 1.000000
       SCCS (0):