User blog comment:MilkyWay90/I'm ready for the easiest OCF!/@comment-32697988-20180821002553/@comment-27513631-20180821231303

Ugh, not an analysis.

An "analysis" is a table of a bunch of rows saying "we can put this through some function that exists and it comes out at this, for a reason I hope is clear to you because it certainly is to me".

Normally, when you do them, you're working with a set of rules in your head. Now, make up a bunch of different terms, do the "analysis" on them, and figure out and write down the rules you came up with.

You're literally two steps away from a proof, now. All you need to do is:

(1) Check that your rules work for every term.

(2) This depends on whether you're trying to prove that the notation is well-founded/getting an upper bound for the strength (2.a) or trying to find the exact strength (2.b)

(2.a) Check that if a reduces to b, the ordinal representing a is less than the one representing b.

(2.b) Also (as well as (2.a)) check that every ordinal is mapped to by some term.

Daunting as it looks, this may even take less time than an average detailed analysis, because you don't have to do hundreds of cases, because you've already written down the general case. Besides that, if you do (1) but not (2) then you've still saved yourself a load of effort because you can just tell people "look at the general case".