MAYBE

Problem:
 minus(x,y) -> if(gt(x,y),x,y)
 if(true(),x,y) -> s(minus(p(x),y))
 if(false(),x,y) -> 0()
 p(0()) -> 0()
 p(s(x)) -> x
 ge(x,0()) -> true()
 ge(0(),s(x)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 gt(0(),y) -> false()
 gt(s(x),0()) -> true()
 gt(s(x),s(y)) -> gt(x,y)
 div(x,y) -> if1(ge(x,y),x,y)
 if1(true(),x,y) -> if2(gt(y,0()),x,y)
 if1(false(),x,y) -> 0()
 if2(true(),x,y) -> s(div(minus(x,y),y))
 if2(false(),x,y) -> 0()

Proof:
 DP Processor:
  DPs:
   minus#(x,y) -> gt#(x,y)
   minus#(x,y) -> if#(gt(x,y),x,y)
   if#(true(),x,y) -> p#(x)
   if#(true(),x,y) -> minus#(p(x),y)
   ge#(s(x),s(y)) -> ge#(x,y)
   gt#(s(x),s(y)) -> gt#(x,y)
   div#(x,y) -> ge#(x,y)
   div#(x,y) -> if1#(ge(x,y),x,y)
   if1#(true(),x,y) -> gt#(y,0())
   if1#(true(),x,y) -> if2#(gt(y,0()),x,y)
   if2#(true(),x,y) -> minus#(x,y)
   if2#(true(),x,y) -> div#(minus(x,y),y)
  TRS:
   minus(x,y) -> if(gt(x,y),x,y)
   if(true(),x,y) -> s(minus(p(x),y))
   if(false(),x,y) -> 0()
   p(0()) -> 0()
   p(s(x)) -> x
   ge(x,0()) -> true()
   ge(0(),s(x)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   gt(0(),y) -> false()
   gt(s(x),0()) -> true()
   gt(s(x),s(y)) -> gt(x,y)
   div(x,y) -> if1(ge(x,y),x,y)
   if1(true(),x,y) -> if2(gt(y,0()),x,y)
   if1(false(),x,y) -> 0()
   if2(true(),x,y) -> s(div(minus(x,y),y))
   if2(false(),x,y) -> 0()
  Open