MAYBE
MAYBE
TRS:
 {
         plus(x, 0()) -> x,
         plus(0(), y) -> y,
        plus(s(x), y) -> s(plus(x, y)),
        times(0(), y) -> 0(),
       times(s(x), y) -> plus(y, times(x, y)),
     times(s(0()), y) -> y,
            div(x, y) -> quot(x, y, y),
          div(0(), y) -> 0(),
    div(div(x, y), z) -> div(x, times(y, z)),
   quot(x, 0(), s(z)) -> s(div(x, s(z))),
   quot(0(), s(y), z) -> 0(),
  quot(s(x), s(y), z) -> quot(x, y, z)
 }
 DUP: We consider a duplicating system.
  Trs:
   {
           plus(x, 0()) -> x,
           plus(0(), y) -> y,
          plus(s(x), y) -> s(plus(x, y)),
          times(0(), y) -> 0(),
         times(s(x), y) -> plus(y, times(x, y)),
       times(s(0()), y) -> y,
              div(x, y) -> quot(x, y, y),
            div(0(), y) -> 0(),
      div(div(x, y), z) -> div(x, times(y, z)),
     quot(x, 0(), s(z)) -> s(div(x, s(z))),
     quot(0(), s(y), z) -> 0(),
    quot(s(x), s(y), z) -> quot(x, y, z)
   }
  Fail