User blog comment:Wythagoras/The nineteenth Busy Beaver number is greater than Graham's Number!/@comment-5529393-20160724100849/@comment-10429372-20160724103048

It certainly isn't trivial. It is pure coincidence that the main algorithm for the third and later group also work for the second group. Honestly, I can't say what I was thinking when I randomly discarded three states of the machine to see whether it was still working.