NO

Problem:
 g(x,x,y) -> y
 g(x,y,y) -> x
 f(x,y,x,y,z) -> f(a(),b(),z,z,z)
 a() -> 0()
 b() -> 0()

Proof:
 Unfolding Processor:
  loop length: 3
  terms:
   f(0(),0(),0(),0(),0())
   f(a(),b(),0(),0(),0())
   f(0(),b(),0(),0(),0())
  context: []
  substitution:
   
  Qed