Toward Interoperability of Minimal Programs

Assumed background: Kolmogoro complexity and Solomonoff induction. Suppose I have some data, and I go looking for the models (i.e. programs) which best compress that data. I find two different programs, and, which both reproduce the data using approximately the same number of bits, and that seems to be roughly the best compression possible. On examination, I find that the two models do totally different things internally.