None of the implementations support negative numbers, but the rules say integer which includes negative numbers, so that should be a legal move.

Negative numbers would break the game by making the number of possible splits infinite. E.g. 1 could split into [-2, 3], [-3, 4], [-4, 5], etc.

It also violates Rule 1 because one of the splits is larger than the original number.

Rules say you can’t ever produce a number greater than the original largest number, so the possibilities will always be finite. (fixed number of ways to make a list of distinct integers that sum to N such that all values are <=M).

You're right in the first sentence, but you're second sentence if we're talking about splitting the largest original number itself that way.

They also say that a given integer should be split into two smaller integers.