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