YES

TRS:

  fac(0()) -> 1()
  fac(s(x)) -> *(s(x),fac(x))
  floop(0(),y) -> y
  floop(s(x),y) -> floop(x,*(s(x),y))
  *(x,0()) -> 0()
  *(x,s(y)) -> +(*(x,y),x)
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  1() -> s(0())
  fac(0()) -> s(0())

linear polynomial interpretations on N:

  fac_A(x1) = 1
  fac#_A(x1) = 5
  0_A = 0
  0#_A = 3
  1_A = 0
  1#_A = 4
  s_A(x1) = 0
  s#_A(x1) = 0
  *_A(x1,x2) = x1
  *#_A(x1,x2) = 2
  floop_A(x1,x2) = x2
  floop#_A(x1,x2) = 3
  +_A(x1,x2) = x1
  +#_A(x1,x2) = 1

precedence:

  1 > 0 > fac = + > s > floop > *