OK. In the while loop, I create a hash whose keys are the words from the list (there is no value, that's why the undef).
Then, I go through the words one by one. For each word, I try all the positions and all possible lengths of its subwords (and I skip the maximal length at position 0, because that would breake the rule #2). For each subword, I do nothing if it has already been printed out (each word should be reported just once). I do nothing if rules #3 or #4 apply. Otherwise, I check whether the subword is itself on the list of words. If it is, I report it and book it as such. And that's it.
The basic idea was this: Comparing each word to all other words would take ages. There would be many comparisons of words that are totally incompatible. How can I reduce the number of comparisons? I do not need all the words, I only need those that are possible for the given word.
As I read the code know, I think it might be optimized a bit further. Instead of caching the reported subwords, you can cache the tested ones (i.e. move the undef three lines up, before the "if"). %reported should be renamed to %checked then.