CP Nautilus

Step 1 - CPFB: Solve the 1x2x3 at dL and permute all remaining corners. The typical strategy is to solve the DL line while permuting all corners. Then add the FL and BL edges. There are a few recognition methods for CP, so choose your favorite.

Step 2 - 2x2x2: Solve the 2x2x2 at dbr. The recommended strategy for building the 2x2x2 is the same as the non-CP version of the method. First build the right side 1x2x2 then add the DB edge. This strategy is great because it is very easy to be efficient when building the 1x2x2 and adding the DB edge is very automatic because there aren't many possibilities. If a user doesn't want to use M slice moves during this step, that is also easy to avoid. Another good strategy for building the 2x2x2 is to first solve the DB edge then build the right side 1x2x2. The DB edge is very easy to solve using just the R r U moveset. Building the right side 1x2x2 can also be accomplished using only the R r U moveset but it is much easier if M slice moves are used.

The primary benefit of the 1x2x2 first strategy is that it is very easy and gives the user a lot of freedom. With the DB edge first strategy the edges that are needed for the right side 1x2x2 can be misoriented. This means the edges have to flipped using slice moves and wide turns while managing the position of the DB edge that was already solved.

Step 3 - EODF: Orient all remaining edges while solving the DF edge. This step is only 55 cases or can be performed intuitively. View EODF algorithms here.

Step 4 - LSLL: During this step you are free to solve the final F2L pair and continue with 2GLL. Or you can use a different LSLL method.

This method is essentially a CP version of the Nautilus LSLL variant.

If CP is planned during inspection, the remaining steps of Nautilus variants have the number of cases drastically reduced and other steps can be combined to allow for fewer looks and more pieces solved at once. Some notes for how this can improve the existing variants:

• LL/ZBLL: ZBLL is reduced to 84 cases and becomes 2GLL.

• LSLL: After EODF, any LSLL method now has many fewer cases.

• CLL+L5E: CLL becomes 7 cases. So doing Winter or Summer Variation means the corners are automatically solved.

• 2GLL+1: Instead of EODB -> Insert pair + CP, 2GLL+1 as in the original variant, it now becomes Shell -> dFR pair + EO -> 2GLL+1. This means better recognition overall and a reduced move-count.

• CX: L5C can now be solved using just 104 algorithms.

• Polar: Many fewer cases for the really advanced variant.

• CLL+2: If CLL+2 is 42 * 6 = ~250 cases, then it now becomes just 7 * 6 = ~40 cases. For COLL+2, even fewer.

• Transformation: Even greater reduction in the number of cases for L5C and improved recognition for transformed corners.

There are likely new variants that would really take advantage of the CP state. One good way may be CX+3. This would solve L5C while solving three edges. If the union system is used to generate this, then it would be maybe ~3-6 * L5C = 300-600 algorithms depending on if all edges are oriented or not.

So far, every CP based method that has been proposed, including the various CPEO 2x2x3 methods and CPLS, are focused on the 2-gen aspect. An important realization, however, is that CP provides additional benefits. These include a dramatic decrease in the number of cases and a decrease in move-count depending on the step.

Vincent Trang proposed a very interesting two-step variant. After CP Shell, the steps would be to solve all five corners and the FR edge then end with L5E. The first step is a lot of algorithms, so it was suggested that the user can place the FR edge at DF or FR to reduce the number of cases. A transformation version of this was also proposed:

1. Place any U layer corner at UBR then do an R turn. This corner doesn't have to be oriented on the U layer before performing the R turn.

2. Orient all corners while solving the FR edge.

3. L5E.