PCMS

PCMS (pairs, CLL, M and S slices) is an advanced method for speedsolving using columns first, designed by Kenneth Gustavsson in late 2008. The method compromises between easy look ahead and low move count (slice metric), and the result is 'decent' for both parts. The first two steps of PCMS leave the cube in a very similar state to the first two steps of Roux method.
Steps:
 Columns:
 Slices:
Contents
Starting the solve
As do most cubers, I usually start from the same side/colour, but if there is one (or more) pair completed in the opposite colour from the scramble, then I use that side. When doing so I only solve columns opposite. These are bidirectional so you just need to turn the cube upsidedown before the slices are solved and you can go into your normal colour from there.
Inspection  this is the key to success. Be able to predict the turns for solving 23 pairs and you will get good times.
Looking ahead for pieces of the pairs while turning is the slowest part of this method, so it really pays to be good at predicting the turns. Use what you have. In some scrambles two corners are solved next to each other. In this case, pair the edges on the opposite side and then put the corners there using D2 (or use a solver to find algs to put them in directly from some easy to set up to positions).
If you cannot see an easy pair from start, do not randomly scan the cube for pieces, rather, disregard certain pieces. There are nine permutations for the edge that all need three moves to be solved. The rest of the positions are two, or possibly even one move to solve. If the corner is oriented in D as in the the image below, and the edge is sitting in one of the darker positions, (assuming it is not solved), then it is a bad pair. All these positions are near the corner, so you can see it pretty easily and then ignore that corner and pick another one.
The bad pairs.
You will soon learn to recognize the rest of the positions, three of which only require a D (or u) move to pair up. The last group that requires two moves consists of eleven different cases. Being able to quickly find the first pair leaves enough inspection time to find at least one more, possibly even two.
Pairs
The move count is dependent on how well you solve the first step. If you look ahead further and create more than one pair before you start to place them, you can make as low as 10 turns for all four pairs sometimes. It is even possible to solve in under 45 moves on average, but not while speedcubing. A low move count is not as important as making sure to not regrip while solving the pairs. This is the part where you can gain speed in this step. For example, place a pair using U Rw U R' rather than (y') R' U R. This avoids cube rotations. Making 1517 turns while speedcubing is normal.
Pairing up is done a bit differently than in Fridrich F2L. First, find a pair, preferably one where the corner is unoriented in the Ulayer, and the edge is in the Dlayer. If the edge is not there, then one in the Ulayer is a second choice because it is easy to place in the D layer using a single slice move. Orient the cube so that the edge is in FD or BD position, and move the corner into position using a U move. Then pair the two pieces using the Mslice. For the pairs where the corner or the edge is in bad position, you have to do some setup moves to fix that, or simply use the CFOP alg for the same pair.
Example:
Scramble:
1.
L2 B F U2 F' L2 B' D F' U2 R D2 L F2 L' D' B2 F U2 
 p1; pieces are good, just do M2 to pair up and (z) to place.
 p2; because only one pair is solved here we can do the next from bottom and up, like this: U L2 to pair and R' U (x) to place it.
 p3; nice corner, edge in Ulayer so setup that one first using (y) M' then U M2 to pair up and U2 B' to place it (temporarly move the Bside to U before the B turn).
 p4; both pieces in position so: (y) U2 M2 to pair up and U R' U2 R to place.
16 moves not counting puzzle rotations, pretty normal.
At bottom of this page you can find some more examples.
CMSLL
CMSLL is pretty much the same as CLL for 2x2x2 (or CF) but in some cases you need to use double layer turns to preserve the pairs, for example R U' R' U' F' U F becomes R U' Rw' U' F' U F. In cases where that does not work any alg optimal for CMLL will do fine but with the advantage that you don't have to AUF the case so it fits with the empty Mslice, here the Sslice is equally good to use.
Algs and all cases you can find at the CxLL pages.
Example:
If we continue from the example for the pairs, then this case is Sune :P
 (y2) R U R' U R U2 R'
Try to look for edges to solve in the next comming step while executing the CLL alg. Advanced it is possible to solve some from inserting slice moves in the CLL, like if it is Sune: R U R' U (M) R U2 R'
Slices
The first part of the second half of the solve is all intuitive, you pair one first layer edge with it's centre and then place it into position. After some parctice this is really easy, no thinking required. It is possible to create more advanced methods than this and use algs for some parts but that is not a good idea, it would only kill the easiness and speed for this part of the solve.
Example:
(Continued from above)
 p1; U' M' to pair (y) M' to place.
 p2; paired! M' U2 M to place.
 p3; paired again, (y') U2 M' to place.
Note that you can solve the third pair before the second using only one move, which would save one U2 but add two cube rotations ((y') p2 (y) p3 (y') L5EO). I usually solve the edge opposite to the first as the second one just to avoid rotations. I think that it is faster on average, especially if you look for that edge while solving the first one. If it is stuck in the D layer, then try to find one edge that faces to the side in the U layer instead. Then the same thing applies: solve the edge opposite to the second as the third to avoid rotations.
L5E: (dunno what name I used at first but it will be L5E from here, that to stick to cubing vocabulary standards =)
Example:
(Continued from above)
 L5EO; U' M' U' M U M' U' M to orient and place FD edge.
 L5EP; UPLL
See L5E for description and algs.
You only need five algs for orientation, but it is a good idea to learn as many as possible that also solve the FD edge. This has two reasons: First is that you can recognize EPLL faster than L5E permutations. (The 5cycles are particularly slow.) The second reason is that you get an EPLL skip 1:12 times. For five oriented edges that number is 1:60.
Note; after I wrote this article I have completed L5EOP, which is the method I mostly use and also did in the examples of this page.
ELL?
If you don't like L5E or already know ELL, it is possible to end the solve by also putting down the last Dlayer edge in the same manner as the other three, and then end in ELL. But I do not recommend it, because recognition of ELL is slow. L5E is faster on average, and you may save a few moves, but it doesn't make up for it.
However, as an extension to PCMS, ELL is the first thing to think of because sometimes you skip the last edge while solving the third one and in some cases it was already skipped from start and you did not see that, so you end up having an ELL. You can still solve all ELL's using L5E, and in some cases even more optimally, but there are good cases in ELL that you would miss.
Summary
The first half of this method, columns, is much harder to master than the slice part, which can be learned fairly easy. Learning CLL can take some time. The algs are not that hard, but the recognition can be. That also applies to solving the pairs in the start. Look ahead is harder than in CFOP because there are more places to look for the edges (D layer).
So, the first steps are where you need to put in more effort if you want to use this method for speedsolving. Expect many pauses before it starts to get fluid. The second part, on the other hand, is where the fun begins, especially if you are good at MUstyle algs. Most of these algs are short, and case recognition is quick. Sometimes it is hard to keep up in the rapid phase. Occasionally a piece becomes solved and you don't know how :D
See also
More examples
Scramble:
2.
L D2 L' D2 L F2 D2 B2 U L' F' L' R F D2 R2 U2 B2 L 
Inspection: One pair (orange/blue) is doable using a single M' but we like to find some more to do before we start. If we think we solve that first pair and also reorient using (z'), then the orange/green is in fine position, it needs a U' and a M to be paired and is then easily placed. Now inspection time is running out so we are pleased with that...
 p1; M' (z') as planned.
 p2; U' M as planned, then U2 L' U (x') to place.
 p3; then we find a red/green corner in front of the eye and the edge is right under it so U' M' to pair up and Rw U R' to place.
 p4; this last pair is looking bad but is not that hard, first orient the cube (y) and then R U' M2 to pair up and U R' to place.
16 STM again, as said, it's the normal.
CLL is mirror diagonal Sune, I'm using the usual Sune + inserts for this one, a COLL actually.
 L' U' L U' (R U') L' (U R') U2 L inserts in parentesis.
Slices:
 p1; M' to pair and then reorient before placement (y) U2 M'
 p2; the opposite to the first is stuck in D so next will be orange; (y) U M' U' M.
 p3; bad, but; (y') M' (y') M' U M (y) M the last turn will go back up again in orientation but trying to see that while going does not work well.
Last five edges:
 L5EO; M' U M U2 M' U' M orients edges and permutes the FD edge.
 L5EP; HPLL
Scramble:
3.
R2 U' B2 F2 L2 B2 R' D2 B R' D F D' U2 B' U' R' B2 L2 
Inspection: No solved pairs and no one move pairs in the D colour so let's look if there is any in the opposite colour and yes, the red/blue one is one turn. Orient the puzzle so it comes to solving position for that pair (x' y') and quickly look if there is one more... red/green will do, it is two moves to pair up:
 p1; D as planned.
 p2; B' M2 as planned, (temp tilt the Bside to U) then U2 R' U (x) to place.
 p3; fine, already paired and easy to place; U' L.
 p4; corner oriented in U, I use an alg for this one but first I need to set up the edge, AUF and orient the puzzle; M' U2 (y')  L' U2 L2 F' L' F ... Yeha, I'm lefty.
16 STM, a little luck and a long pair in the end made it an average solve, expect the last pair to use more turns than the rest, often it is not easier to solve here than in normal F2L.
CLL is bars Bruno, I use a COLL also for this one, a combo of Niklas and Sune.
 (y) R' U L U' R U' L' U' L U' L' ... lefty alg again =)
Slices:
Now, because I solved in the opposite colour from start I AUF and turn the puzzle upsidedown before I start the second half of the solve; U' (x2)
 p1; orange in front, centre in back so; U2 M U (y) M
 p2; skipped!.
 p3; (y') M U' M' easy =)
Last five edges:
 L5EO; U M' U M the finest case.
 L5EP; ZPLL
That one was pretty nice, easy cases in the end, as it often is using this method.