YES

Problem:
 -(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))))

Proof:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   lt#(s(x),s(y)) -> lt#(x,y)
   div#(s(x),s(y)) -> -#(x,y)
   div#(s(x),s(y)) -> div#(-(x,y),s(y))
   div#(s(x),s(y)) -> lt#(x,y)
   div#(s(x),s(y)) -> if#(lt(x,y),0(),s(div(-(x,y),s(y))))
  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))))
  Usable Rule Processor:
   DPs:
    -#(s(x),s(y)) -> -#(x,y)
    lt#(s(x),s(y)) -> lt#(x,y)
    div#(s(x),s(y)) -> -#(x,y)
    div#(s(x),s(y)) -> div#(-(x,y),s(y))
    div#(s(x),s(y)) -> lt#(x,y)
    div#(s(x),s(y)) -> if#(lt(x,y),0(),s(div(-(x,y),s(y))))
   TRS:
    -(x,0()) -> x
    -(0(),s(y)) -> 0()
    -(s(x),s(y)) -> -(x,y)
    div(0(),y) -> 0()
    div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
    if(true(),x,y) -> x
    if(false(),x,y) -> y
    lt(x,0()) -> false()
    lt(0(),s(y)) -> true()
    lt(s(x),s(y)) -> lt(x,y)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     -(x,0()) -> x
     -(0(),s(y)) -> 0()
     -(s(x),s(y)) -> -(x,y)
    interpretation:
     [div#](x0, x1) = x0 + 0,
     
     [if#](x0, x1, x2) = x1 + 0,
     
     [lt#](x0, x1) = 2x0,
     
     [-#](x0, x1) = 1x0 + 0,
     
     [div](x0, x1) = x0 + 0,
     
     [if](x0, x1, x2) = 1x0 + 2x1 + x2 + 0,
     
     [true] = 2,
     
     [false] = 2,
     
     [lt](x0, x1) = 2x0 + 1x1 + 1,
     
     [s](x0) = 4x0 + 4,
     
     [-](x0, x1) = 1x0,
     
     [0] = 3
    orientation:
     -#(s(x),s(y)) = 5x + 5 >= 1x + 0 = -#(x,y)
     
     lt#(s(x),s(y)) = 6x + 6 >= 2x = lt#(x,y)
     
     div#(s(x),s(y)) = 4x + 4 >= 1x + 0 = -#(x,y)
     
     div#(s(x),s(y)) = 4x + 4 >= 1x + 0 = div#(-(x,y),s(y))
     
     div#(s(x),s(y)) = 4x + 4 >= 2x = lt#(x,y)
     
     div#(s(x),s(y)) = 4x + 4 >= 3 = if#(lt(x,y),0(),s(div(-(x,y),s(y))))
     
     -(x,0()) = 1x >= x = x
     
     -(0(),s(y)) = 4 >= 3 = 0()
     
     -(s(x),s(y)) = 5x + 5 >= 1x = -(x,y)
     
     div(0(),y) = 3 >= 3 = 0()
     
     div(s(x),s(y)) = 4x + 4 >= 5x + 2y + 5 = if(lt(x,y),0(),s(div(-(x,y),s(y))))
     
     if(true(),x,y) = 2x + y + 3 >= x = x
     
     if(false(),x,y) = 2x + y + 3 >= y = y
     
     lt(x,0()) = 2x + 4 >= 2 = false()
     
     lt(0(),s(y)) = 5y + 5 >= 2 = true()
     
     lt(s(x),s(y)) = 6x + 5y + 6 >= 2x + 1y + 1 = lt(x,y)
    problem:
     DPs:
      
     TRS:
      -(x,0()) -> x
      -(0(),s(y)) -> 0()
      -(s(x),s(y)) -> -(x,y)
      div(0(),y) -> 0()
      div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
      if(true(),x,y) -> x
      if(false(),x,y) -> y
      lt(x,0()) -> false()
      lt(0(),s(y)) -> true()
      lt(s(x),s(y)) -> lt(x,y)
    Qed