CPLS
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CPLS (short for Corner Permutation and Last Slot) is a substep used to solve the last F2L slot (usually FR) and permute the last layer corners while preserving EO. CPLS leaves the solver with a 2-gen last layer, which may be solved in one look using 2GLL (84 algs) or in two using OCLL+EPLL (11 algs).
Although seemingly hard to recognize, CPLS can be very beneficial, especially for one-handed solvers if fast 2-generator algorithms are used.
History
CPLS was proposed by Baian Liu in 2009. The name initially only referred to the CPLC subset which solves the F2L corner + CP.
However, CPLS here refers to solving the last F2L pair + CP because the LS suffix in cubing often indicates the last pair being solved (compare ZBLS,OLS, VLS, WVLS etc.) and thus prevents confusion for people unfamiliar with CPLS. If one wants to clearly distinguish between the "original CPLS" and the "new CPLS", they can be referred to as CPLC and Full CPLS, respectively.
Subsets
Full CPLS is grouped into subsets depending on the F2L case they solve and then by their corner permutation.
Naming by CP case
Below, only the subsets for the individual F2L cases are listed. The naming for the different CPs of each F2L case is obtained by adding the following F2L letters to the subset, depending on the CP of the U layer corners.
S
Solved CP |
D
Diagonal swap |
R
Adjacent swap on R |
B
Adjacent swap on B |
L
Adjacent swap on L |
F
Adjacent swap on F |
Naming by F2L case
CPLC
CPLC, the "original CPLS", stands for Corner Permutation Last Corner and solves the last LL corner and CP. It consists of 26 algorithms and is grouped into the following six subsets depending on the F2L corner, which is the same classification that is used for CLS:
C
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I
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Im
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-
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+
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O
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Recognition
Although the seemingly difficult recognition may appear to be a possible disadvantage of CPLS, the following system due to Stachu Korick works well.
- AUF the last F2L corner to URF, and note the group (O etc).
- For each of the three U-layer corners, locate the sticker clockwise from its U-layer sticker. This is best done in a fixed order (say UFL, UBL, UBR).
- Pretend that the face containing the each sticker is of the same color. The required corner permutation is the permutation of the corresponding faces necessary to regain the standard color scheme.
Scramble: x R' U R U' R' U R U' R' U R U' x' (yellow on top, orange in front)
The last F2L corner is already at URF. This is an O case. The stickers clockwise from U-layer (yellow) stickers are at FLU (red), LUB (green), BRU (orange). Pretending that F = red, L = green, and B = orange, the required permutation swaps F and B, represented by FLU and BRU corners. Thus we want O with diagonal swap (both diagonal swaps have the same effect), which is x (U R' U' R)*3 x'. We may write this case as [O BLF], meaning the true color of the B face is on F, that of L on L, and F on B.
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CPLE
CPLE stands for Corner Permutation Last Edge and solves the last F2L edge and CP. It only covers F2L case 25 and consists of only 6 algorithms.
Example Solves
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This recognition method is best illustrated with example solves. Standard color scheme is assumed throughout. Scramble with white on top (U) and green in front (F). Notes in square brackets by Stachu Korick.
Scramble 1: D' B' D2 F2 R F' L' R B L' F' U' R' B F2 U R2 D L2 D2 U' B R' F2 D'
A Petrus approach
2x2x2: x2 D B' R' D2 L2 (5/5) 2x2x3: x' y D R D' U' L' U L (7/12) [Tthis sets up for an Im case later on] EO: y U M' U M (4/16) F2L: x y U2 R' U' R U R' U' R2 U2 R' (10/26) [ewww] CPLS (Im FBL): y2 U R' F2 R D' L' U2 L' U' L2 D (11/37) 2GLL (Pi Ua1): y (y) R U2 R2 U2 R U R2 U R2 U' R2 U2 R' U2 R(16/53) AUF: U2 (1/54)
Scramble 2: L2 F' L2 F L' D B D2 U2 L2 D L' R B' L2 U B2 R2 D2 R B2 D U2 B' F'
A RH OH ZZ approach
EOCross: L B' R' U D F R D R' D R' (11/11) BL slot: U2 R U R' L U L' (7/18) FL slot: L2 U2 L U L' U L2 (7/25) BR slot: U R' U' R U' R' U R (8/33) FR edge: R U R' (3/36) [It kills me not to do CLS for this case :(] CPLS setup: U2 (1/37) CPLS (O): y U2 z' U L' D2 L U' L' D2 z (8/45) 2GLL (T Ub2): z' U L2 U' L' U L' U' L U L U' L U L2 U' (15/60) AUF: L2 (1/61, or 57 with cancellations)
Scramble 3: L' R' B F U B2 D2 F2 L F2 D U' B' U D2 F2 B L2 R2 B U2 B' D2 U2 R
A CFOP approach Not working
Cross: x2 F D L2 U2 L F' (6/6) BL slot: F' U2 F L U' L' (6/12) FR slot: U R U2 R' U R' F R F' (9/21) BR slot: U' R' U2 R2 B' R' B (7/28) ELS setup: y U (1/29) ELS: R U' R' F' U2 F (6/35) CPLS (+): U' U' y R' U L' U' R U L (9/44) 2GLL (Pi Ub3): y' (y) R U2 R2 U' R' U R U' R' U' R' U' R' U2 R U2 (15/59, or 56 with cancellations)
