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 KBO with weight

  w0 = 1
  w(f) = 0
  w(*) = 0
  w(g) = 0
  w(one) = 1

and precedence:

  * > f > g > one
)