MAYBE

Problem:
 p(0()) -> s(s(0()))
 p(s(x)) -> x
 p(p(s(x))) -> p(x)
 le(p(s(x)),x) -> le(x,x)
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 minus(x,y) -> if(le(x,y),x,y)
 if(true(),x,y) -> 0()
 if(false(),x,y) -> s(minus(p(x),y))

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