# CPLS

 CPLS [[Image:]] Information Proposer(s): Baian Liu, ?, ? Proposed: 2009? Alt Names: none Variants: none Subgroup: No. Algs: 26 Avg Moves: ~10 Purpose(s): Previous state: unknown Next state: unknown
 Previous cube state -> CPLS step -> Next cube state The CPLS step is the step between the Previous cube state and the Next cube state.

CPLS (short for Corner Permutation and Last Slot) is a substep used to solve the final F2L corner (usually DFR) and permute the last-layer corners while preserving the corresponding F2L edge and EOLL. If used when only the last F2L corner, EPLL, CPLL, and COLL remain, CPLS leaves just EPLL and COLL, which may be solved in 2-generator. Although seemingly hard to recognize, CPLS can be very beneficial, especially for one-handed solvers if fast 2-generator algorithms are used.

A two-step solution to EPLL and COLL requires only 11 algorithms: 7 for OCLL, which leaves 4 EPLL cases. One-step solution, known as 2GLL, has 84 cases. Note that this is also referred to as ZZ-d.

## History

CPLS was proposed by Baian Liu in 2009.

## Learning Approach

CPLS is naturally divided into the subsets - +, O, I, Im, and C, the same classification used for CLS. The first three sets have 6 algorithms each, the next two have 3 each, and the final set has only 2. One recommended order, for ease of learning and recognition, is C, O, I, Im, -, +.

## Recognition

Although the seemingly difficult recognition may appear to be a possible disadvantage of CPLS, the following system due to Stachu Korick works well.

1. AUF the last F2L corner to URF, and note the group (O etc).
2. 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).
3. 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.

## Example Solves

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)
```