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())

max/plus interpretations on N:

  fac_A(x1) = max{2, -6}
  fac#_A(x1) = max{7, 7}
  0_A = 1
  0#_A = 0
  1_A = 1
  1#_A = 6
  s_A(x1) = max{1, -1 + x1}
  s#_A(x1) = max{4, 2}
  *_A(x1,x2) = max{2, -5, -6}
  *#_A(x1,x2) = max{1, 3, 7}
  floop_A(x1,x2) = max{0, 7, 5 + x2}
  floop#_A(x1,x2) = max{8, 15, 12 + x2}
  +_A(x1,x2) = max{2, x1, -6}
  +#_A(x1,x2) = max{7, 5 + x1, 7}

precedence:

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