MAYBE

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 int(x,y) -> if(le(x,y),x,y)
 if(true(),x,y) -> cons(x,int(s(x),y))
 if(false(),x,y) -> nil()

Proof:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   int#(x,y) -> le#(x,y)
   int#(x,y) -> if#(le(x,y),x,y)
   if#(true(),x,y) -> int#(s(x),y)
  TRS:
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   int(x,y) -> if(le(x,y),x,y)
   if(true(),x,y) -> cons(x,int(s(x),y))
   if(false(),x,y) -> nil()
  Usable Rule Processor:
   DPs:
    le#(s(x),s(y)) -> le#(x,y)
    int#(x,y) -> le#(x,y)
    int#(x,y) -> if#(le(x,y),x,y)
    if#(true(),x,y) -> int#(s(x),y)
   TRS:
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
   Open