YES

Problem:
 f(g(x,y),x,z) -> f(z,z,z)
 g(x,y) -> x
 g(x,y) -> y

Proof:
 DP Processor:
  DPs:
   f#(g(x,y),x,z) -> f#(z,z,z)
  TRS:
   f(g(x,y),x,z) -> f(z,z,z)
   g(x,y) -> x
   g(x,y) -> y
  EDG Processor:
   DPs:
    f#(g(x,y),x,z) -> f#(z,z,z)
   TRS:
    f(g(x,y),x,z) -> f(z,z,z)
    g(x,y) -> x
    g(x,y) -> y
   graph:
    
   Qed