2GLL (short for 2-Generator Last Layer) is a fraction of ZBLL. ZBLL is meant to orient and permute corners of the last layer while permuting the edges, and comes up to hefty 493 cases. Taking the subset of this that does not permute the corners, and instead only orients the corners and permutes the edges, these cases can be reduced to 85, while also having each case be able to be solved by a "2-generator" algorithm (one that uses only 2 algorithms, in this case usually the R and U faces.
2GLL is very useful when one has a system for permuting the LL corners and orienting the LL edges prior to getting to the last layer. One system that achieves rooting off of CFOP would be to do the cross, three F2L pairs, ELS, and lastly CPLS. While this could be a good system to branch off of CFOP, most would agree that the system would work better on methods which naturally orient the edges before getting to the final slot of F2L such as ZZ or Petrus. Another method to use during CFOP to accomplish 2GLL would be to orient edges while doing 'normal' F2L, perhaps having two or more algs for each F2L case, influencing different edge orientations.
Much like in ZBLL and COLL, the cases of 2GLL can be divided into seven individual sets to learn and recognize by. These sets are typically called Sune, Anti-Sune, H (or Double-Sune), Pi, U, T, L, and EPLL. Each 2GLL is typically recognized by the COLL of the case, followed by the edge cycle that is present (see EPLL. Typically, there are 12 cases per [[COLL[[, but some can be eliminated due to mirrors and the like.
For every subset, one can recognize their case by the means of the following system:
1. Recognize the corner orientation case. (one of 7)
1.5? - Some people prefer to AUF right now in order to have their corners not only in their relatively correct spot, but also in their *actual* correct spot. As in, rather than having the corners a U2 away from being correctly permuted, they would do a d2, then recognize from there, or something along those lines. Because a good percentage of the 'good' algs have AUFs and/or initial rotations anyway, it doesn't make all that much of a difference, so if it helps you to recognize this way, do so.
2. Recognize the edge cycle by looking only at the FU and RU stickers in relation to the UFR piece.
3. Apply the corresponding algorithm.
Step 1 should be fairly easy to recognize, as there are only seven possible cases, and if you have used another LL technique, then you have most likely had to recognize corner orientation before. When you see the case, simply adjust the upper-most face in order to get the case into the angle you typically recognize from, and continue to the next step.
Step 2 is a tiny bit more complicated to recognize, but once it is gotten used to, it can really be quite easy. Since there are a possible of 12 edge permutations (assuming that the puzzle is solvable and the corners are permuted) one has to be prepared for all 12.
Here is one system to recognize these in: - If you see that both the FU and RU edges are correctly positioned between corners that have been pre-permuted, then this is a "good" case, meaning that all of the edges are correctly positioned.
- If you see that both the FU and RU edges are opposite colors of what they should be (red/orange or blue/green on the standard color scheme) then this is an "H perm" case.
- If you see that the FU piece and RU piece should be switched with each other (a visible 2-cycle) then you have "Z1," one of two possible Z perms. - If you see that FU needs to go to LU while RU needs to go to BU, then you have the other Z perm, "Z2."
If the case does not follow into any of the above, then - For the remaining 8 cases, the U perms, without rotating the cube, the solver should ask themselves the following: --"Is this cycle going clockwise or anti-clockwise?" --"Where is the edge that is correct?"
Both of these questions can be answered by figuring out the following: --"Where does the FU sticker need to be in respect to the corner permutation?" --"Where does the RU sticker need to be in respect to the corner permutation?"
Simply put, try to trace a 3-cycle of edges in the last layer. The piece that does not belong combined with the direction of the cycle is a great way to recognize and notate the cycle.
As a quick example, scramble a standard 3x3x3 Rubik's Cube with the following: R' U2 R U R' U R U' R' U' R U' R' U2 R
Firstly, look at the corner orientation. You should be able to find this as a Headlights case. Put these headlights in the back - if you ever decide to learn COLL or ZBLL, this is how you will probably recognize headlights cases, so it's a good idea to start that way now! Next note that this is not a "good", H, or Z case, and therefore must be a Uperm of sorts. Next, note that this is a clockwise U perm - one that does not cycle RU. That's it. Right then, you should be able to apply your alg, AUF, and slam your cube down, stopping the timer.
For this case, y R' U2 R U R' U R U R' U' R U' R' U2 R is a nice alg. Success.