Lastly, it's exhausting replying to all this. Can you condense your posts a little in future?

Sorry. I try very hard to not write so much, but the large amount of text just reflects how much I have to share (honestly).

I always try to be as concise as I can. Even then, there is at least 2 times as much that I can also mention, but I don't.

Your download links are broken.

I just clicked them and it worked. It's weird, but after a few seconds, the download links appear. For some reason, you have to wait longer for the dark color version than the light color version. So try again, and let me know if you can access them after waiting a little longer.

What kind of algs, comms? Do I already know most of them?

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Recognition sounds fine but the algs don't sound very fast.

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Are they fast?

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Like, lots of PLL algs suck

See the document attached to

this post (if you haven't already by now). As you will see, most of the 2 2-cycles are just conjugations of r2 (or l2). I have cleverly made all twelve 1 2-cycle and 1 3-cycle algorithms (on page 14 of the document) from one base alg, so I believe I at least took care of the ugliest PLL cases. I have recently edited the document again because I realized that 66 algs are needed, not 56. But the new algs I just added are 3-cycles which you already know.

And, the algorithms I placed in that document aren't the fastest for all of the cases presented. For the 2 2-cycle algs, I tried to focus on using only 8 base algorithms to handle all 29 cases.

Since for the largest group of 2 2-cycles I used the alg

[l2 U' F2 U': l2](9), if you don't find that very fast, here are two alternatives:

[Lw2 F2 U L2 U: l2] (11)

[Rw2 F2 L U' L' U': r2](13)

(You can alter these in the same manner that I did with the 9 mover and still get algs for all cases in that group).

Also, note that the other case formed from these algorithms by inverting the single quarter turn faces of U has a fast form for the 9 mover

[Lw2 U F2 U: l2](9).

With the exception of most 13 btm and all 15 btm algs that cancel to 11 btm and 13 btm, respectively, due to (L R') and (L' R), I believe I have exhaustively searched all possible algorithms of length (7-13 btm) of the form [A:B] generated by <L,R,U,F,l2,r2,Rw2,Lw2>, and I have to say that the algorithms I have provided in the document for the 2 2-cycles are unique. I grabbed all solutions that begin and end with wide turns, if they had single inner layer turns as equivalents. Hence, they are as good as they get for speed. (This holds true for probably most of the F3L algs too, as many algs in the text document below were used for them).

In fact, I have attached a text document which shows 2,472 algs.

View attachment 2_2-Cycles.txt
If you're overwhelmed, don't worry. I had to sort out the algorithms to be able to use them for F3L. (Sadly I ended up not using most, and I had already found most of the ones I used before I did this exhaustive search).

View attachment Algs_Sorted.pdf
Note that for the group of 2,416 algorithms, I only bothered to sort most of the algorithms that began with either r2 or Rw2 and that conjugated r2 (only 1/4 of 2,416). I also eliminated petty equivalents for the 7 and 9 btm move algs.

All in all, many of the algorithms give the same result on the cube, whether they are mirrors, or if they affect pieces in different faces. In addition, a big chunk of the algorithms cannot be used for F3L or ELL, as they affect wings on opposite faces or in positions which require additional conjugation to be useful (more moves).

There's no point recognizing and working out the alg solve two edges in one when you can execute two fast comms with no pauses faster. (Of course, I'd love you to prove me wrong)

I agree with you for a portion of the cases. However, cases that require 9-10 moves are definitely more debatable. Probably if both wings are in the U-Layer, it's not worth memorizing (for speed purposes, but definitely for move count), but if both wings are in the E-Layer or one wing is in the U-Layer and the other is in the E-Layer, it definitely becomes more tempting (to me at least).

For example, here are a few of the cases that I highly doubt can be handled faster with two algs.

Case 16-6

[z'Lw2U'F2U':l2]
Case 9-15

[z'Rw2U'F2U':r2]
Case 11-8

[x:U'l'r'UR'U'lrUR]
Case 4-13

[x':R2U'l2rUR'U'l2r'UR']
etc.

This seems... unfriendly as a speedsolving approach.

Maybe so, but I mention in the document that 14 base algs are used to form algs for all 211 cases. (Note also that the number of cases we really can say are distinct is 99.) For the cases in the U-Layer and cases in the U-Layer and E-Layer, only 1/4 of the algs need to be memorized because we use the trivial U, U' and U2 conjugations which still keep the move count <=12 btm.

EDIT:

And if you don't count cases which can be achieved with trivial conjugations of U, U' and U2 as well as reflections, inverses and cube rotations, there are 39 distinct algs. (And of course these algs are interrelated as well due to my statement about the fact that 14 base algs are used to make all 211 cases).