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 EKBO with interpretations on natural numbers

  f_A(x1,x2) = x2 + 1
  *_A(x1,x2) = x1 + x2
  g_A(x1,x2) = x1 + 1
  one_A = 1
  f#_A(x1,x2) = x1 + x2
  *#_A(x1,x2) = x1 + x2
  g#_A(x1,x2) = x1 + x2
  one#_A = 0

weights

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

and precedence:

* > f > g > one
)