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))))
  LPO Processor:
   argument filtering:
    pi(0) = []
    pi(-) = 0
    pi(s) = [0]
    pi(lt) = []
    pi(false) = []
    pi(true) = []
    pi(if) = [1,2]
    pi(div) = [0]
    pi(-#) = 0
    pi(lt#) = 0
    pi(if#) = 0
    pi(div#) = 0
   precedence:
    div > s > lt > div# ~ if# ~ lt# ~ -# ~ if ~ true ~ false ~ - ~ 0
   problem:
    DPs:
     
    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))))
   Qed