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))))

linear polynomial interpretations on N:

  -_A(x1,x2) = x1
  -#_A(x1,x2) = 0
  0_A = 0
  0#_A = 2
  s_A(x1) = x1 + 1
  s#_A(x1) = 3
  lt_A(x1,x2) = 1
  lt#_A(x1,x2) = 0
  false_A = 1
  false#_A = 1
  true_A = 1
  true#_A = 1
  if_A(x1,x2,x3) = x2 + x3
  if#_A(x1,x2,x3) = 0
  div_A(x1,x2) = x1 + 1
  div#_A(x1,x2) = x1 + x2 + 3

precedence:

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