Start by encoding each item to sort into an expression consisting of factors of prime numbers so that it's reversible. Conway chain notation of the factors wou

Start by encoding each item to sort into an expression consisting of factors of prime numbers so that it's reversible. Conway chain notation of the factors would make a nice pessimistic next step, though that might violate your termination requirement as there won't be enough Planck volumes in the known universe to represent anything beyond the first few terms. :)