HK is a really interesting method but the HKPLL set is bad and HKOLL is mostly just inserting edge>>OLL or vice versa. If you're going to do the CxLL>>L5E variant you might as well use a method that arrives there more efficiently and ergonomically such as Nautilus-L5E and db APB-CDRLL.
Actually most of the algs I looked at were RrUF and really quick. I'm not switching I was just looking
 
Does anyone know if there is an alg sheet for solving 4x4 pll parity cases in one alg (instead of solving parity then pll, just one single alg to finish it all)?
It not, is there a way someone can help me try to create one (of its possible)?
Thanks.
I know this is a while ago but here is how to make your own sheet:

Step 1: Go to this site: https://jperm.net/algs/4x4/pll

Step 2: Screenshot all the algorithms

Step 3: Crop the screenshots in the photo apps as necessary

Step 4: Copy and paste each of the photos into a google doc

Step 5: Print the google doc



Then you will have all d the cases printed out on a piece of paper. In other words, a literal sheet. This can work for any alg set too.
 
If you have (R U R’ U R U2 R’) inversing would be doing it backwards (R U2 R’ U’ R U’ R’) I am not 100% sure what reversing is, but from videos that mention it, I think it could mean just inverting the signs without making the order backwards. (R’ U’ R U’ R’ U2 R)
 
What is the difference between reversing and inversing moves?
One of them (inverting) has a generally understood meaning while the other one (reversing) does not.

Inverting means you do two things: read the move sequence from right to left, and also reverse all the move directions (clockwise becomes anticlockwise and vice versa).

Reversing can mean any of these:
1. Same thing as inverting. Probably the most common usage, since "inverse" (in the mathematical sense) is not in the common lexicon.
2. Reading the move sequence right to left, but without reversing the move directions. E.g. R U R' U R U2 R' becomes R' U2 R U R' U R.
3. Reading the move sequence left to right, but reversing the move directions. (I had never seen this until now but I guess it's an option.)

Sense 2 is sometimes useful for RU 2-gen algs; it captures what happens when you both invert and mirror the alg. Under some weak assumptions, an alg that's regripless from home grip will have a mirror-inverse that's also regripless from home grip.
 
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