MAYBE
MAYBE
TRS:
 {
                                      isEmpty(cons(x, xs)) -> false(),
                                            isEmpty(nil()) -> true(),
                                               isZero(0()) -> true(),
                                              isZero(s(x)) -> false(),
                                         head(cons(x, xs)) -> x,
                                         tail(cons(x, xs)) -> xs,
                                               tail(nil()) -> nil(),
                                    append(cons(y, ys), x) ->
  cons(y, append(ys, x)),
                                          append(nil(), x) -> cons(x, nil()),
                                                    p(0()) -> 0(),
                                                 p(s(0())) -> 0(),
                                                p(s(s(x))) -> s(p(s(x))),
                                                  inc(0()) -> s(0()),
                                                 inc(s(x)) -> s(inc(x)),
  if(false(), false(), false(), xs, ys, xs2, ys2, zs, zs2) ->
  addLists(xs2, ys2, zs),
   if(false(), false(), true(), xs, ys, xs2, ys2, zs, zs2) ->
  addLists(xs, ys, zs2),
         if(false(), true(), b, xs, ys, xs2, ys2, zs, zs2) ->
  differentLengthError(),
         if(true(), false(), b, xs, ys, xs2, ys2, zs, zs2) ->
  differentLengthError(),
          if(true(), true(), b, xs, ys, xs2, ys2, zs, zs2) -> zs,
                                      addLists(xs, ys, zs) ->
  if(
    isEmpty(xs), isEmpty(ys), isZero(head(xs)), tail(xs), tail(ys),
    cons(p(head(xs)), tail(xs)), cons(inc(head(ys)), tail(ys)), zs,
    append(zs, head(ys))
  ),
                                           addList(xs, ys) ->
  addLists(xs, ys, nil())
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                                        isEmpty(cons(x, xs)) -> false(),
                                              isEmpty(nil()) -> true(),
                                                 isZero(0()) -> true(),
                                                isZero(s(x)) -> false(),
                                           head(cons(x, xs)) -> x,
                                           tail(cons(x, xs)) -> xs,
                                                 tail(nil()) -> nil(),
                                      append(cons(y, ys), x) ->
    cons(y, append(ys, x)),
                                            append(nil(), x) ->
    cons(x, nil()),
                                                      p(0()) -> 0(),
                                                   p(s(0())) -> 0(),
                                                  p(s(s(x))) -> s(p(s(x))),
                                                    inc(0()) -> s(0()),
                                                   inc(s(x)) -> s(inc(x)),
    if(false(), false(), false(), xs, ys, xs2, ys2, zs, zs2) ->
    addLists(xs2, ys2, zs),
     if(false(), false(), true(), xs, ys, xs2, ys2, zs, zs2) ->
    addLists(xs, ys, zs2),
           if(false(), true(), b, xs, ys, xs2, ys2, zs, zs2) ->
    differentLengthError(),
           if(true(), false(), b, xs, ys, xs2, ys2, zs, zs2) ->
    differentLengthError(),
            if(true(), true(), b, xs, ys, xs2, ys2, zs, zs2) -> zs,
                                        addLists(xs, ys, zs) ->
    if(
      isEmpty(xs), isEmpty(ys), isZero(head(xs)), tail(xs), tail(ys),
      cons(p(head(xs)), tail(xs)), cons(inc(head(ys)), tail(ys)), zs,
      append(zs, head(ys))
    ),
                                             addList(xs, ys) ->
    addLists(xs, ys, nil())
   }
  Fail