YES

TRS:

  p(s(x)) -> x
  fac(0()) -> s(0())
  fac(s(x)) -> times(s(x),fac(p(s(x))))

max/plus interpretations on N:

  p_A(x1) = max{5, -4 + x1}
  p#_A(x1) = max{7, 6}
  s_A(x1) = max{9, 7 + x1}
  s#_A(x1) = max{0, -4}
  fac_A(x1) = max{9, -1}
  fac#_A(x1) = max{4, -2 + x1}
  0_A = 1
  0#_A = 5
  times_A(x1,x2) = max{0, -1, x2}
  times#_A(x1,x2) = max{3, 3, -3 + x2}

precedence:

  fac > s > p = 0 = times