Conjugated CxLL is a way to solve the last five corners (L5C) using only 42 CxLL algorithms by conjugating them with an R move. (The used CxLL depends on the method.) It is a subset of Transformation.
It was invented independently by both James Straughan for his A2 method based on the development of a CLL transformation table where Conjugated CLL is used and by Joseph Briggs for his 42 method based on Roux where Conjugated CMLL is used.
- When only five corners remain (four on U and one in DFR), orient one of them and place it at UBR.
- Perform an R move to bring all of the other four corners to the U layer.
- Recognize the case and perform the correct CxLL algorithm.
- Recognition works by associating multiple cases with one CxLL algorithm (see the last three links in #External links)
- The used CxLL subset is dependant on the method. For example in 42, where edges in U and M do not need to be preserved, CMLL is used. However in Zipper where the F2L-1 cube state needs to be preserved, 3x3 CLL may be used.
- AUF so that the corners are an R' away from being solved and then perform the R'.
Comparison with L5C
- The amount of algorithms is reduced from 614 to only 42
- More moves are required
- Having to orient one corner and doing an R move makes this not fully one look
- Recognition still needs to be learned for all cases
- L4C (which has 84 algorithms and is usually considered one of the worst ZBLL subsets) is required for solving L5C as a last step (when everything except for five corners is solved)
- CxLL algorithm sets that also twist a corner (TCLL, TCMLL, etc.) can be used so that the oriented corner in UBR isn't required anymore, which also lowers movecount a bit. However, this is at the price of 128 instead of 42 algorithms.