YES

(VAR x0 x1 x2 x y)
(RULES
  *(x0,*(x1,x2)) -> *(*(x0,x1),x2)
  i(*(x0,x1)) -> *(i(x1),i(x0))
  *(*(x0,i(x1)),x1) -> x0
  *(x,i(x)) -> one()
  *(*(x0,x1),i(x1)) -> x0
  *(x0,one()) -> x0
  d(x0,x1) -> *(x0,i(x1))
  *(i(x0),x0) -> one()
  i(one()) -> one()
  *(one(),y) -> y
  i(i(y)) -> y
)

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

  d_A(x1,x2) = x1 + x2 + 1
  one_A = 1
  i_A(x1) = x1
  *_A(x1,x2) = x1 + x2 + 1
  d#_A(x1,x2) = x1 + x2
  one#_A = 0
  *#_A(x1,x2) = x2

and precedence:

d > i > * > one
)