MAYBE

Problem:
 minus(0(),y) -> 0()
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 plus(0(),y) -> y
 plus(s(x),y) -> plus(x,s(y))
 zero(s(x)) -> false()
 zero(0()) -> true()
 p(s(x)) -> x
 div(x,y) -> quot(x,y,0())
 quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0())))
 if(true(),x,y,z) -> p(z)
 if(false(),x,s(y),z) -> quot(minus(x,s(y)),s(y),z)

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   plus#(s(x),y) -> plus#(x,s(y))
   div#(x,y) -> quot#(x,y,0())
   quot#(x,y,z) -> plus#(z,s(0()))
   quot#(x,y,z) -> zero#(x)
   quot#(x,y,z) -> if#(zero(x),x,y,plus(z,s(0())))
   if#(true(),x,y,z) -> p#(z)
   if#(false(),x,s(y),z) -> minus#(x,s(y))
   if#(false(),x,s(y),z) -> quot#(minus(x,s(y)),s(y),z)
  TRS:
   minus(0(),y) -> 0()
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   plus(0(),y) -> y
   plus(s(x),y) -> plus(x,s(y))
   zero(s(x)) -> false()
   zero(0()) -> true()
   p(s(x)) -> x
   div(x,y) -> quot(x,y,0())
   quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0())))
   if(true(),x,y,z) -> p(z)
   if(false(),x,s(y),z) -> quot(minus(x,s(y)),s(y),z)
  Open