YES

Problem:
 f(0(),1(),X) -> f(X,X,X)
 g(X,Y) -> X
 g(X,Y) -> Y

Proof:
 DP Processor:
  DPs:
   f#(0(),1(),X) -> f#(X,X,X)
  TRS:
   f(0(),1(),X) -> f(X,X,X)
   g(X,Y) -> X
   g(X,Y) -> Y
  EDG Processor:
   DPs:
    f#(0(),1(),X) -> f#(X,X,X)
   TRS:
    f(0(),1(),X) -> f(X,X,X)
    g(X,Y) -> X
    g(X,Y) -> Y
   graph:
    
   Qed