Conjugated CxLL
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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[1] where Conjugated CLL is used and by Joseph Briggs for his 42 method based on Roux where Conjugated CMLL is used.
Contents
Steps
 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 F2L1 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
Advantages
 The amount of algorithms is reduced from 614 to only 42
Disadvantages
 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)
Improvements
 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.