MAYBE

Problem:
 minus(x,x) -> 0()
 minus(0(),x) -> 0()
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 quot(x,y) -> if_quot(minus(x,y),y,le(y,0()),le(y,x))
 if_quot(x,y,true(),z) -> divByZeroError()
 if_quot(x,y,false(),true()) -> s(quot(x,y))
 if_quot(x,y,false(),false()) -> 0()

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   le#(s(x),s(y)) -> le#(x,y)
   quot#(x,y) -> le#(y,x)
   quot#(x,y) -> le#(y,0())
   quot#(x,y) -> minus#(x,y)
   quot#(x,y) -> if_quot#(minus(x,y),y,le(y,0()),le(y,x))
   if_quot#(x,y,false(),true()) -> quot#(x,y)
  TRS:
   minus(x,x) -> 0()
   minus(0(),x) -> 0()
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   quot(x,y) -> if_quot(minus(x,y),y,le(y,0()),le(y,x))
   if_quot(x,y,true(),z) -> divByZeroError()
   if_quot(x,y,false(),true()) -> s(quot(x,y))
   if_quot(x,y,false(),false()) -> 0()
  Open