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Thanks for asking! (but I bet you're sorry you did)
You're not wrong there :) :)
Its situations like this where MathML or equivalent would be really nice, since you could just give me the forumlae :)
In essence, what I understood was the following:
For every permutation 1->n check every permutation 1->n to see if it is equivalent according to the rules. If it is, mark it as such.
Results: a set of groups of permutations who are deemed equivalent.
Are the rules transitive?
My head generated psuedocode something like this (no efficiency or anything, just a general algorithm):
But that only works if the rules are both transitive and symmetric (you hint that they are but I may be reading it wrong)
I would be interested in the contents of the rules 1->3 if they're not going to make my head ache :)