YES

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

(COMMENT
Termination is shown by KBO with weight

  w0 = 2
  w(*) = 0
  w(f) = 1
  w(g) = 1

and precedence:

  * > f > g
)