YES

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

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

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

and precedence:

one > g > * > f
)