YES

(VAR x)
(RULES
  *(*(s(y()),s(y())),fac(+(*(s(y()),y()),y()))) -> fac(*(s(y()),s(y())))
  s(+(*(s(y()),y()),y())) -> *(s(y()),s(y()))
  *(s(0()),s(0())) -> fac(s(0()))
  *(0(),s(y())) -> *(0(),y())
  *(s(x),fac(x)) -> fac(s(x))
  fac(0()) -> s(0())
  +(*(x,y()),x) -> *(x,s(y()))
  *(x,0()) -> 0()
  +(x,s(y())) -> s(+(x,y()))
  +(x,0()) -> x
)

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

  +_A(x1,x2) = x1
  0_A = 0
  s_A(x1) = 0
  y_A = 0
  *_A(x1,x2) = 0
  fac_A(x1) = 0
  +#_A(x1,x2) = x1 + x2
  0#_A = 0
  y#_A = 0

weights

  w0 = 1
  w(+) = 1
  w(0) = 2
  w(s) = 1
  w(y) = 1
  w(*) = 0
  w(fac) = 2

and precedence:

fac > + > s > * > y > 0
)