Add one more species to a reaction network and the number of reachable states can square. Add another, and it cubes. This is the state-space explosion, and it is the central obstacle of stochastic model checking: before you can prove anything about a CTMC you often have to materialize it, at least partly.

The explorer enumerates every state of the selected network up to a cap on the molecule counts, counts reactions between them, and reports how the count grows. Exact methods (prefix trees instead of hash tables, as in my prefix-tree paper) fight the size of this explosion; partial exploration sidesteps it entirely. Try raising the cap and watch which network becomes expensive first.