YES

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

(COMMENT
Termination is shown by LPO with precedence:

  g > f > i > * > 1
)