User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130619110333/@comment-5150073-20130619140820

I already specified w*2 = w+w as the result of rules A2 and A3. They must be applied before all other (if possible).

By Rule A2:

w*2 = w*1+w

By Rule A3:

w*1+w = w+w

As for Cantor's normal form, it doesn't tells how to determine a_1 > a_2 > ... > a_m, so we need a special algorithm for it, which gets more and more complex when we get further by the ordinals.