> You only need to run N steps where N is the number of possible states. It's at most N steps - the machine can return to a prior state long before that happen

> You only need to run N steps where N is the number of possible states. It's at most N steps - the machine can return to a prior state long before that happens, which would also prove that it's non-halting. Of course the memory requirements to do that make it purely theoretical - but so too is exhaustive execution (due to time requirements). https://en.wikipedia.org/wiki/Busy_beaver#Exact_values_and_lower_bounds https://en.wikipedia.org/wiki/Busy_beaver#Exact_values_and_l...