Well to some extent there is a guarantee on that. If they're small enough to be represented as integers in raw Perl, then they're limited in size and my solution is faster than the NP-complete one beyond some (generally not very large) number of numbers.

Of course that guarantee is not particularly useful, because the program won't necessarily run on a real machine without running out of RAM.

At which point I point out my weasel words, "almost certainly not NP-complete" and say that my "almost certainly" was based on my strong suspicion that most concrete programming problems which would result in this kind of question coming up involve small integers. With the critical question being how small.