MAYBE

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

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