YES

(VAR x0 x1 x y z)
(RULES
  i(*(x0,x1)) -> *(i(x1),i(x0))
  i(one()) -> one()
  *(*(x0,x1),i(x1)) -> x0
  i(i(x0)) -> x0
  *(x0,i(x0)) -> one()
  *(x0,one()) -> x0
  *(*(x0,i(x1)),x1) -> x0
  div(x,y) -> *(x,i(y))
  *(x,*(y,z)) -> *(*(x,y),z)
  *(i(x),x) -> one()
  *(one(),y) -> y
)

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

  *_A(x1,x2) = x1 + x2 + 1
  one_A = 1
  i_A(x1) = x1
  div_A(x1,x2) = x1 + x2 + 2
  *#_A(x1,x2) = x2
  one#_A = 0

weights

  w0 = 1
  w(*) = 0
  w(one) = 1
  w(i) = 0
  w(div) = 1

and precedence:

i > div > * > one
)