YES

(VAR x0 x1 x2 x y)
(RULES
  f(*(x0,x1)) -> g(x0)
  *(x0,*(x1,x2)) -> *(x0,g(x1))
  g(*(x0,x1)) -> f(x1)
  *(*(x2,x0),x1) -> *(f(x0),x1)
  *(x0,f(x1)) -> *(x0,x1)
  *(x0,g(x0)) -> g(x0)
  g(f(x0)) -> f(x0)
  f(g(x0)) -> g(x0)
  *(f(x0),x0) -> f(x0)
  f(f(x0)) -> f(x0)
  g(g(x0)) -> g(x0)
  *(f(x0),g(x0)) -> x0
  *(g(x),y) -> *(x,y)
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  *_A(x1,x2) = x1 + x2 + 2
  f_A(x1) = x1 + 1
  g_A(x1) = x1 + 1
  *#_A(x1,x2) = x2
  f#_A(x1) = 0

weights

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

and precedence:

g > * > f
)