Regan's algorithm cannot prove that you did not cheat; it can only fail to prove that you cheated.

The question that Regan's algorithm is this: "Did you cheat?"

If the algorithm comes back with "Yes," then you cheated. But it cannot come back with "No." It can only come back with "I failed to prove that you were cheating."

You need another hypothesis: "Did you not cheat?" But this is an impossible test.