"Always halts after 1024 steps or fewer" is a rather stricter constraint than "halts after BB(2^10^12) steps". https://en.wikipedia.org/wiki/Busy_beaver https:

"Always halts after 1024 steps or fewer" is a rather stricter constraint than "halts after BB(2^10^12) steps". https://en.wikipedia.org/wiki/Busy_beaver https://en.wikipedia.org/wiki/Busy_beaver