YES

(VAR x0 y x)
(RULES
  f(x0,x0) -> one()
  f(one(),x0) -> x0
  g(x0,one()) -> x0
  g(x0,x0) -> one()
  *(one(),y) -> y
  *(x,one()) -> x
  g(*(x,y),y) -> x
  f(x,*(x,y)) -> y
)

(COMMENT
Termination is shown by LPO with precedence:

  * > f > g > one
)