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(),
                              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(), y, xs, ys, x) -> sumList(ys, x),
   if(false(), true(), y, xs, ys, x) -> sumList(xs, y),
         if(true(), b, y, xs, ys, x) -> y,
                      sumList(xs, y) ->
  if(
    isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)),
    inc(y)
  ),
                             sum(xs) -> sumList(xs, 0())
 }
 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(),
                                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(), y, xs, ys, x) -> sumList(ys, x),
     if(false(), true(), y, xs, ys, x) -> sumList(xs, y),
           if(true(), b, y, xs, ys, x) -> y,
                        sumList(xs, y) ->
    if(
      isEmpty(xs), isZero(head(xs)), y, tail(xs),
      cons(p(head(xs)), tail(xs)), inc(y)
    ),
                               sum(xs) -> sumList(xs, 0())
   }
  Fail