User blog comment:Planterobloon/Noob question about the FGH/@comment-28606698-20171214171932/@comment-30754445-20171215025139

Basically this.

I'd like to add that this gets much much easier with practice. The first few times you try to do such an analysis you'll have to think carefully at every step of the way, but after a while it becomes second nature to you.

It is also important to realize that doing this efficiently (and correctly) also requires a good understanding of the ordinals you're working with. For the small ones like ω×n+m this is the easy part. But for (say) a ωω ω -level notation, you first need to be really really familiar with how ωω ω  itself works.