YES

(VAR x0 x1 x y z)
(RULES
  g(1(),*(x0,x1)) -> *(g(1(),x1),g(1(),x0))
  *(*(x0,g(1(),x1)),x1) -> x0
  *(*(x0,x1),g(1(),x1)) -> x0
  *(g(1(),x0),x0) -> 1()
  *(x,g(1(),x)) -> 1()
  g(1(),g(1(),x0)) -> x0
  i(x0) -> g(1(),x0)
  f(x0,x1) -> g(x0,*(g(1(),x1),x0))
  *(1(),x0) -> x0
  *(x0,1()) -> x0
  g(1(),1()) -> 1()
  *(x,*(y,z)) -> *(*(x,y),z)
)

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

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

and precedence:

f > i > g > * > 1
)