User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130619110333/@comment-1605058-20130620154501

Rule A1 is completely wrong. First of all, it fails for almost all pairs of finite ordinals. For infinite ones, w+w2=w3≠w2, w*w2=(w^2)*2≠w2, w^w2>w2. I can't see any constrains on alpha and beta, so these are counterexamples