User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130619110333/@comment-5529393-20130620112907

It looks like the only change is that you specified m > 2, which doesn't help. Again, set \(\alpha_1 = \omega + 1, \alpha_2 = \omega, \beta_1 = \beta_2 = 1\), and it fails.