YES

TRS:

  -(x,0()) -> x
  -(0(),s(y)) -> 0()
  -(s(x),s(y)) -> -(x,y)
  lt(x,0()) -> false()
  lt(0(),s(y)) -> true()
  lt(s(x),s(y)) -> lt(x,y)
  if(true(),x,y) -> x
  if(false(),x,y) -> y
  div(x,0()) -> 0()
  div(0(),y) -> 0()
  div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))

max/plus interpretations on N:

  -_A(x1,x2) = max{1, x1, -11}
  -#_A(x1,x2) = max{29, 28 + x1, 43}
  0_A = 13
  0#_A = 24
  s_A(x1) = max{22, 7 + x1}
  s#_A(x1) = max{0, 2 + x1}
  lt_A(x1,x2) = max{14, 1, -1}
  lt#_A(x1,x2) = max{27, 26 + x1, 43}
  false_A = 2
  false#_A = 23
  true_A = 2
  true#_A = 1
  if_A(x1,x2,x3) = max{21, 7 + x1, 8 + x2, x3}
  if#_A(x1,x2,x3) = max{29, 29, 0, 7 + x3}
  div_A(x1,x2) = max{20, 12 + x1, 8}
  div#_A(x1,x2) = max{23, 21 + x1, 25}

precedence:

  div > - = s = if > 0 > true > lt > false