YES

(VAR x1 x0 x2 x y z)
(RULES
  *(f(*(x1,x0)),x2) -> *(f(x0),*(f(x1),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 = 1
  g_A(x1) = x1
  f_A(x1) = 1
  *#_A(x1,x2) = x2
  one#_A = 0

and precedence:

g > f > one > *
)