MAYBE
Trs:
 {                         inc(s(x)) -> s(inc(x)),
                            inc(0()) -> s(0()),
                          p(s(s(x))) -> s(p(s(x))),
                           p(s(0())) -> 0(),
                              p(0()) -> 0(),
                         tail(nil()) -> nil(),
                   tail(cons(x, xs)) -> xs,
                   head(cons(x, xs)) -> x,
                        isZero(s(x)) -> false(),
                         isZero(0()) -> true(),
                      isEmpty(nil()) -> true(),
                isEmpty(cons(x, xs)) -> false(),
         if(true(), b, y, xs, ys, x) -> y,
   if(false(), true(), y, xs, ys, x) -> sumList(xs, y),
  if(false(), false(), y, xs, ys, x) -> sumList(ys, x),
                             sum(xs) -> sumList(xs, 0()),
                      sumList(xs, y) -> if(isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)), inc(y))}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open