Super Super Optimization - How to Prove Equivalents

The goal of super optimization is to generate, for example, the shortest instruction sequence that has the same behavior. To do that we need to prove equivalents between two arbitrary programs. And so what people did initally they said, ok, let's not look at arbitrary programs. Lets just look at straight line instruction sequences with no branches and no loops. Can we do that? Then initially people also didn't know how to do that. So there was a form of testing between the two sequences that was applied in the first paper on supertimization, which sn 19 82, by masalin. After that, peoplehve worked on verification. They came oh, we have tools that can prove