MAYBE

Problem:
 ge(x,0()) -> true()
 ge(0(),s(x)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 div(x,y) -> ify(ge(y,s(0())),x,y)
 ify(false(),x,y) -> divByZeroError()
 ify(true(),x,y) -> if(ge(x,y),x,y)
 if(false(),x,y) -> 0()
 if(true(),x,y) -> s(div(minus(x,y),y))

Proof:
 DP Processor:
  DPs:
   ge#(s(x),s(y)) -> ge#(x,y)
   minus#(s(x),s(y)) -> minus#(x,y)
   div#(x,y) -> ge#(y,s(0()))
   div#(x,y) -> ify#(ge(y,s(0())),x,y)
   ify#(true(),x,y) -> ge#(x,y)
   ify#(true(),x,y) -> if#(ge(x,y),x,y)
   if#(true(),x,y) -> minus#(x,y)
   if#(true(),x,y) -> div#(minus(x,y),y)
  TRS:
   ge(x,0()) -> true()
   ge(0(),s(x)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   div(x,y) -> ify(ge(y,s(0())),x,y)
   ify(false(),x,y) -> divByZeroError()
   ify(true(),x,y) -> if(ge(x,y),x,y)
   if(false(),x,y) -> 0()
   if(true(),x,y) -> s(div(minus(x,y),y))
  Open