MAYBE
MAYBE
TRS:
 {
               lt(x, 0()) -> false(),
            lt(0(), s(y)) -> true(),
           lt(s(x), s(y)) -> lt(x, y),
             plus(x, 0()) -> x,
            plus(x, s(y)) -> s(plus(x, y)),
         help(x, s(y), c) -> if(lt(c, x), x, s(y), c),
            quot(x, s(y)) -> help(x, s(y), 0()),
  if(false(), x, s(y), c) -> 0(),
   if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y))))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                 lt(x, 0()) -> false(),
              lt(0(), s(y)) -> true(),
             lt(s(x), s(y)) -> lt(x, y),
               plus(x, 0()) -> x,
              plus(x, s(y)) -> s(plus(x, y)),
           help(x, s(y), c) -> if(lt(c, x), x, s(y), c),
              quot(x, s(y)) -> help(x, s(y), 0()),
    if(false(), x, s(y), c) -> 0(),
     if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y))))
   }
  Fail