# Playing With Roux Orientations



## cubacca1972 (Jan 29, 2009)

I am starting this thread because I hijacked another (sorry about that).

I came up with the idea of parking the UL and UR edge cubies in the DF and DB positions (either order), and solving one of eleven possible orientation patterns, so that all remaining edges are oriented, and UL and UR are still in DF and DB positions, ready to be slotted home with U (or U', or U2), M2, then U or U'.

The original algorithms that I found via Ron's sticker mode solver were:

M U' M U M' U2 M U' M U' M (11,12)
M U M' U2 M U M' (7,8)
M' U2 M' U2 M' U' M U2 M U2 M (11,15)
M' U M' U2 M' U M' U M U' M' (11,12)
M' U M U' M' U2 M (7,8)
M U' M U2 M U' M U' M' U M (11,12)
M U' M' U M U2 M' (7,8)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M U' M' U' M2 (9,12)
M U M U M U M (7,7)
M' U M' U M' U M2 U' M U2 M' U' M (13,15)

Athefre was able to find several amazing shortcuts to several of the algorithms as above, and we learned about some blind spots that computer solvers have when looking for optimal solutions to the orientation step with the roux method.


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## Athefre (Jan 29, 2009)

cubacca1972 said:


> Athefre said:
> 
> 
> > That was the part I hated most, I didn't even bother memorizing the corner sequences until 2 years after I started using the method.
> ...




I completely understand your idea, but I don't know much programming either so I wouldn't be much help with that.



cubacca1972 said:


> Athefre said:
> 
> 
> > Just to update:
> ...




In your original solution, the two misoriented edges have to be at UF/UB before performing the sequence, in the first alternative they have to be at UL/UR.


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## cubacca1972 (Jan 29, 2009)

Oops. I was worried for a second that the whole solution set might have sub cases where the algs didn't work. I am relieved.

As far as the pseudocode goes, I think I could get some of the subroutines working, but I have no ideas how to write a subroutine that would start with 1 alg, then check the next one, etc. Sigh.


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## Athefre (Jan 29, 2009)

cubacca1972 said:


> As far as the pseudocode goes, I think I could get some of the subroutines working, but I have no ideas how to write a subroutine that would start with 1 alg, then check the next one, etc. Sigh



I probably won't be able to help much further. With shortcuts and the new 7.7 average one can probably average 14 moves total using your LSE method.

Place UL/UR: 2 (Results of an average - 0, 3, 1, 1, 2, 3, 2, 2, 3, 3, 1, 1)
Orient: 7.7
Permute: 1.5 (UL/UR) + 4 (M edge permutation has an average of 4 moves, you could talk about the chance of having the first move be a U2 but that doesn't remove anything from the average, either way there's going to be a U or U' after placing UL/UR in their correct slots)
Shortcuts: -1 possibly, really depends on what you choose to use.

I'll probably now work on describing the suitable optimizationss, unless you already see them.


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## cubacca1972 (Jan 30, 2009)

Athefre said:


> I probably won't be able to help much further. With shortcuts and the new 7.7 average one can probably average 14 moves total using your LSE method.
> 
> Place UL/UR: 2 (Results of an average - 0, 3, 1, 1, 2, 3, 2, 2, 3, 3, 1, 1)
> Orient: 7.7
> ...



Thanks for all the work you put in to this system. You definitely get major credit for finding all those optimizations. 

The algorithm list as it stands now:

M' U2 M' U M U M' U' M' (9,10)
M U M' U2 M U M' (7,8)
M' U2 M' U2 M' U' M U2 M U2 M (11,15)
M U2 M' U M U M U2 M (9,11)
M U' M' U' M (5,5)
M' U2 M U' M' U' M' U2 M' (9,11)
M' U M U M' (5,5)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M' (5,7)
M U M U M U M (7,7)
M' U M' U M U M' U2 M' U M (11,12)

I don't see any further optimizations yet, as I do not have enough experience yet with Roux. When you know a system cold, and you no longer have to concentrate on the actual solve, its way easier to let your eyes wander and notice new patterns.

For now, I will concentrate on algorithm crunching. On the upside, I don't think I will have to test drive all of the possible 7 move algorithms. If my logic isn't failing me, then:

When I start with a "solved state" for this system (UL and UR in D layer, all 6 oriented) the pattern is symmetrical.

If I search all algorithms that start with the move M, anything useful I find will have a mirror algorithm that starts with M'.

Therefore, there is no need to search the algorithms that start with M'.

If I complete the 7 move and 5 move search by brute force, then any remaining potential shortcuts for the 2 remaining 11 move algorithms will either be found, or be exactly 9 moves long.

If one or both are 9 moves long, I won't brute force search manually. I will try to write that program.


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## gogozerg (Jan 30, 2009)

This thread reminds me a lot talks I had with Josef Jelinek some time ago.

He was looking for a way to make the "last 6 edges" a 2-look process.That's why he decided to put UL and UR edges in U and D layers, a rather costless starting position requiring at most 1 move (rarely 2).

I had discarded the idea of considering UL and UR edges before orienting, except for special cases, because I thought a simple orientation is easy and fast to learn and anticipate. And while orienting, you have extra time to localize L and R stickers.

By the way, Josef had a small Java program made for optimizing "edges last" endings. Quite useful.

In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.

There are a few possible ways of solving the edges rather efficiently (14-15 moves). The old standard "corners-first" strategy (solve UL or UR edge, then solve the other while orienting) is one of them.

By mixing techniques, you could average 12 moves.
(And of course, there are some other possible FM tricks)

The problem is, how to be fast? No need to learn a sequence that is 2 move shorter if you waste 2 seconds detecting when to use it.

I thought the best was to have an efficient basic method, and then use shortcuts for special cases that can be immediately detected (some orientations ending with non oriented centers, or the old standard strategy when an edge is already solved for instance).

The goal for this step is to consistently average sub-3.


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## cubacca1972 (Jan 31, 2009)

gogozerg said:


> In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.



I hadn't considered that. Once I definitively find the optimal algorithms for all of the cases, I will try both ways- original, and original minus the last 2 moves, and perhaps minus the last M move only. I am not very speedy though. I get most of my kicks by exploring different solving methods.



gogozerg said:


> There are a few possible ways of solving the edges rather efficiently (14-15 moves). The old standard "corners-first" strategy (solve UL or UR edge, then solve the other while orienting) is one of them.



The hallmark of my preferred solving methods is my aversion to learning a lot of algorithms. This is why I like corners first, permuting all U and D corners in one algorithm (vs. Direct solving D corners, then 41 algorithms to solve the U corners). 

I am approaching this particular orientation phase from a corners first mindset. If you solve UR, then solve UL + orient the M slice, you need 21 algorithms down cold:

LU edge is at DF: 8 cases, plus their mirrors = 16 algorithms
LU is in place but flipped: 2 cases = 2 algorithms
LU is "accidentally" solved when RU is solved: 2 adjacent M edges flipped, 2 diagonal flipped, all 4 flipped= 3 algorithms.

This doesn't include special cases where 2 or 4 M edges are flipped in place.

This method is very good, but already starts to grate on my own personal "number of algorithms to know cold" tolerance.



gogozerg said:


> By mixing techniques, you could average 12 moves.
> (And of course, there are some other possible FM tricks)
> 
> The problem is, how to be fast? No need to learn a sequence that is 2 move shorter if you waste 2 seconds detecting when to use it.
> ...



I agree that there is always room for improvement on speed by adding special cases algorithms to you repetoire. I made a point in the hijacked thread that the more special cases you add, the more the system shifts away from the speed end of the spectrum to the FMC end.

I don't know how it is for you, but if I step away from the cube for a few months, or weeks, or even days sometimes, I forget certain algorithms. For corners, I end up having to do multiple sunes to orient the U layer corners for example. 

On the other hand, if you are immersed in speed solving, you obviously retain more through constant practice, and would therefore know your base algorithms cold, and would therefore have a much higher special case algorithm tolerance.


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## Athefre (Jan 31, 2009)

cubacca1972 said:


> gogozerg said:
> 
> 
> > In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.
> ...




I had saw his reply earlier but didn't have time to make my own reply, but you said just about everything I was planning on saying 



gogozerg said:


> This thread reminds me a lot talks I had with Josef Jelinek some time ago.




Finally, I was hoping you would come here to help. You are the true master of this method. I wonder why 



gogozerg said:


> In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.




I thought that was obvious so I didn't tell him about that, I figured he already noticed that it was one of the simpler shortcuts and was already using it.

Also, do you see any way to shorten any of cubacca's sequences? It's easy to find lots of faster alternatives that have the same amount of moves (M'U2M'U2M'UM'U2M'U2M' is faster than the original).



gogozerg said:


> The goal for this step is to consistently average sub-3.




Do you average sub-3 in Step 4 yet? What besides what is on your page do you use? The best average of 12 I've been able to do is 3.01 seconds, sub-3 doesn't _look_ that far away but it _feels_ like I will never get there.


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## blah (Jan 31, 2009)

gogozerg said:


> That's why he decided to put UL and UR edges in U and D layers, a rather costless starting position requiring at most 1 move (rarely 2).



Sorry if I'm dumb or missing something, but I don't see how this requires at most 1 move?!


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## gogozerg (Jan 31, 2009)

cubacca1972 said:


> The hallmark of my preferred solving methods is my aversion to learning a lot of algorithms.
> ...
> I agree that there is always room for improvement on speed by adding special cases algorithms to you repetoire. I made a point in the hijacked thread that the more special cases you add, the more the system shifts away from the speed end of the spectrum to the FMC end.
> ...
> On the other hand, if you are immersed in speed solving, you obviously retain more through constant practice, and would therefore know your base algorithms cold, and would therefore have a much higher special case algorithm tolerance.



I agree with you, 100%. Except what I personnaly don't like is the number of stupid sequences to learn, not algorithms which I love. ;-)
That's why at first I decided to use an easy orientation substep you can figure out in a few minutes. I wish I had find how to deal with corners at some point in a more elegant way...
That's why when learning the old "corners-first" method, I tried to see how it was working in order to learn as few as possible (http://web.archive.org/web/20050111065826/grrroux.free.fr/method/Step_4.html).
In Josef's first phase, I agree there's a lot to learn, and your way makes it much more simple. Try to see now how good it is for speed.



Athefre said:


> Finally, I was hoping you would come here to help.


Since you arrived before, I fear there's nothing left for me!

Off-topic:



Athefre said:


> Do you average sub-3 in Step 4 yet? What besides what is on your page do you use? The best average of 12 I've been able to do is 3.01 seconds, sub-3 doesn't _look_ that far away but it _feels_ like I will never get there.


I think you're faster than me. Never been sub-3.
By the way, timing conditions are important and controversial. In order to make it look more representative of a speed solve I try not to analyze the situation in details and stop the timer with hands flat. I think I naturally use optimizations 1a 3a 6e 9a, and 2a 2b 4d when possible.
With bionic fingers real speed cubers have, I think sub-3 is possible, and sub-5 for steps 3 and 4 is achievable.



blah said:


> Sorry if I'm dumb or missing something, but I don't see how this requires at most 1 move?!


http://rubikscube.info/lastsix2look.php


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## blah (Jan 31, 2009)

gogozerg said:


> blah said:
> 
> 
> > Sorry if I'm dumb or missing something, but I don't see how this requires at most 1 move?!
> ...



I really _was_ dumb after all!  Didn't read clearly, thought you were talking about something else, never mind that


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## cubacca1972 (Jan 31, 2009)

> Originally Posted by gogozerg
> In your list of sequences, I would just drop the last 2 moves to make it look more simple, since the final M* is rather useless (chances for optimization with the next substep are 25%), and the U* before is just about aligning UL and UR.





> I thought that was obvious so I didn't tell him about that, I figured he already noticed that it was one of the simpler shortcuts and was already using it.



I am not seeing the shortcuts yet, or even test driving the method in solves right now. I am still obsessing about searching for shorter algorithms for the last 2 cases with 11 moves (maybe shorter ones for the 9 move algorithms).

As far as speed goes, (stealing a term from a Futurama episode) I have what the speedcubing community would refer to as "stupid fingers".


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## cubacca1972 (Jan 31, 2009)

The current algorithm list:

M' U2 M' U M U M' U' M' (9,10)
M' U M U2 M' U M (7,8)
M' U2 M' U2 M' U M' U2 M' U2 M' (11,15)
M U2 M' U M U M U2 M (9,11)
M U' M' U' M (5,5)
M' U2 M U' M' U' M' U2 M' (9,11)
M' U M U M' (5,5)
M' U' M' U M U' M (7,7)
M' U2 M' U2 M' (5,7)
M' U M' U M' U M' (7,7)
M' U M' U M U M' U2 M' U M (11,12)

Algorithms 2, 3 and 10 have been revised to be a bit more finger friendly. Patterns 2 and 10 now have UB and UL flipped, instead of UF and UR.


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## gogozerg (Feb 1, 2009)

I think you won't find shorter sequences for cases 3 and 11.

(Just in case you're interested in additional tricks:
These cases are not as bad as they look, since with the right initial U adjustment, you can directly orient all edges and solve UL+UR)


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## Athefre (Feb 2, 2009)

gogozerg said:


> I think you won't find shorter sequences for cases 3 and 11.




I figured that, but I hoped there could at least be something shorter for number 3. I tried Cube Solver and it gives 9 move solutions, but they have lots of F2 and M2, not worth it.


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## Emblem62 (Feb 3, 2009)

hey i need some help with roux. i hav a pretty good understanding of the cube and can grasp most concepts. however i dont understand the edge orientation part of roux. i know what it means for a cubie to be oriented and i know how to find which cubies are oriented and which arent. my only problem is fixing the bad edges using only M and U slices.


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## cubacca1972 (Feb 3, 2009)

Emblem62 said:


> hey i need some help with roux. i hav a pretty good understanding of the cube and can grasp most concepts. however i dont understand the edge orientation part of roux. i know what it means for a cubie to be oriented and i know how to find which cubies are oriented and which arent. my only problem is fixing the bad edges using only M and U slices.



I am a newbie with the Roux method as well. I did play with it for a while, and can give you a beginner's perspective on it.

Basically, note which cubies are flipped, according to Roux's definitions on this page:

http://grrroux.free.fr/method/Step_4.html

Next, turn the U layer so that the flipped edges form one of the 9 patterns on that page.

Do the move associated with that pattern.

If there are still flipped edges, repeat the process:

Turn U until the pattern matches one of the nine patterns listed.

Do the move associated with that pattern.

Repeat until all six edges are oriented. Because the LU and RU edges behave slightly differently than the M edges, you won't get the exact same pattern every time you do do one of these iterations.

The first and fifth pattern associated with the M'UM' move have mirror images from front to back. Just do the mirror algorithm MU"M for those.

You should be able to orient all six edges with a maximum of 3 iterations.


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## cubacca1972 (Feb 3, 2009)

I am now attempting to write a program to search algorithms.

Its a painful process so far, but much less painful than testing all possible algorithms of 7 moves or 9 moves. I managed to explore all 7 move algorithms that start with M, but just don't have the heart to do all of the M2 group. The 9 move set is just way too many to do manually.


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## cubacca1972 (Feb 7, 2009)

cubacca1972 said:


> The current algorithm list:
> 
> M' U2 M' U M U M' U' M' (9,10)
> M' U M U2 M' U M (7,8)
> ...



I have just confirmed (the hard way) that these are the optimal algorithm lengths for all 11 cases. What I did was use Ron's cube solver program to "solve" with the whole U layer blanked out, and with DF and DB set as flipped, oriented, or just one flipped. The program checked for all cases without checking centers. Then I manually checked each one in the 7 or 9 move range for the five patterns with 9 or 11 moves. While I didn't find any shorter algorithms, I was able to practice the optimal solutions whenever I reset my cube to try the next algorithm on the list.

Nothing left to do now except get them memorized. Once again, thank you to Athefre for finding the optimal cases for this system.


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## gogozerg (Feb 7, 2009)

cubacca1972 said:


> M' U2 M' U2 M' U M' U2 M' U2 M' (11,15)


M'UMU2MUM'U2MU'M (or symmetrical friend) in only 13-SQTM long.


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## Athefre (Feb 7, 2009)

gogozerg said:


> cubacca1972 said:
> 
> 
> > M' U2 M' U2 M' U M' U2 M' U2 M' (11,15)
> ...



It's slightly harder to memorize but definitely is faster than mine.

M'UM'UMUMUM'UM' is very nice too.


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## cubacca1972 (Feb 7, 2009)

Athefre said:


> gogozerg said:
> 
> 
> > cubacca1972 said:
> ...



I think I have been too hasty in printing out my cheat sheet. Nice alternatives. I think I will have to reprint, or edit with my pen .

I still have a hard time pulling off M smoothly. I do M' by pulling at the B facelet of DB with my left ring finger, and M2 by first pulling with my left ring finger, then pulling again with my left middle finger.

What is the least clumsy way of doing M? Right now, I tend to do (L M) L', using my right thumb to catch the M layer while I do L'.


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## gogozerg (Feb 7, 2009)

Athefre said:


> M'UM'UMUMUM'UM' is very nice too.


Much better!


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## Athefre (Feb 7, 2009)

cubacca1972 said:


> I still have a hard time pulling off M smoothly. I do M' by pulling at the B facelet of DB with my left ring finger, and M2 by first pulling with my left ring finger, then pulling again with my left middle finger.
> 
> What is the least clumsy way of doing M? Right now, I tend to do (L M) L', using my right thumb to catch the M layer while I do L'.



That's the way most people do it. But for M, some use r'R, some use lL'. Bob Burton has said a couple of times that he uses his thumb to push FD.

Since we are talking about faster solutions now:

2. M'UM'U2M'U'M'

4. M'U2M'UM'UM'U2M'

5. MUM'UM

6. M'U2MUM'UM'U2M'

8. M'UM'U'MUM

Didn't spend much time on them, but they are faster than the originals. Set up Case 3 then do E'M'EM, annoying isn't it?.


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## cubacca1972 (Feb 8, 2009)

The new revised list (revised):

1. M' U2 M' U M U M' U' M' (9,10)
2. M' U M' U2 M' U' M' (7,8)
3. M' U M' U M U M U M' U M' (11,11)
4. M' U2 M' U M' U M' U2 M' (9,11)
5. M U M' U M (5,5) A rotation instead of a reflection of case 7.
6. M' U2 M U M' U M' U2 M' (9,11)
7. M' U M U M' (5,5)
8. M' U M' U' M U M (7,7)
9. M' U2 M' U2 M' (5,7)
10. M' U M' U M' U M' (7,7)
11. M' U M' U M U M' U2 M' U M (11,12)



> That's the way most people do it. But for M, some use r'R, some use lL'. Bob Burton has said a couple of times that he uses his thumb to push FD.



I've looked at BB's suggestion to push at FD. I can't quite figure out how to complete the turn (ie, align the layers in preparation for a U move) without contorting my hand position/grip.

I am going to experiment between doing lL' , and doing about a 1/8th of L', pulling at UF with my left thumb, and realigning both layers with my left hand.


> Set up Case 3 then do E'M'EM, annoying isn't it?.



I have wondered about E layer moves. I think that they would likely be more ergonomic than F layer moves.


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## cubacca1972 (Aug 1, 2010)

I have been revisiting an old idea I was playing with when I used to do corners first, and checking its feasibility with Roux.

The idea is to solve the final 6 edges in 2 steps.

Step 1

Solve RU and place the LU edge in the LU slot, but flipped.

Step 2

Orient LU and solve the M slice, with 1 of 24 algorithms.

The rationale behind placing LU in the flipped position in Step 1 is to force the orientation pattern of the M edges into one of two patterns: one flipped or 3 flipped. This seems to help a bit with pattern recognition. 

If you were to direct solve RU and LU, there would be 28 different algorithms for Step 2. For the cases with 2 adjacent edges flipped, there would be eight 3 edge cycles to learn, which could get confusing, as you would also have eight other 3 edge cycles to learn,

For Step 2, all you need to do is park the odd M edge at UF, identify where it belongs by comparing it to the U and F centers, and identify the edge at DF. The UB and DB edges don't need to be considered, as they can only be in one position (you can't swap 2 edges, and since you know UF and DF, knowing the BU and BD edges give you no additional information). In fact, you don't even need to know what permutation pattern you are looking at (3 cycle, double diagonal swap, double adjacent swap, permuted)-just identify the front 2 edges and execute the right algorithm.

You will have to adjust the M slice in 3/4 cases, but that is trivial.

I looked at my old algorithms when I worked this system out a few years ago, and wasn't sure if the algorithms were any good. I searched them again with cube explorer 5.0 and found much better algorithms.

The first column identifies which edge is at UF. The second column identifies which edge is at DF

UF Oriented, Remaining M Edges Flipped

UF DF M' U M' U M' U M' U (8f*)
UF DB U' M U M' F2 U' M' U F2 (9f*)
UF UB U M' U2 M U M U' M U (9,10)
DF UF U' M U M2 U2 M U M' U (9,11)
DF DB U M' U' M U2 M2 U' M U' (9f*)
DF UB U' M U' M U' M U M U2 (9,10)
DB UF M' U' M U M U M U' (8f*)
DB DF U M' U' M' U' M' U (7f*)
DB UB U M' U M2 U2 M' U M U M' U2 (11,14)
UB UF U M' U' M' U' M' U' M2 U2 (9f*)
UB DF U' M U2 M' U M' U' M' U' (9f*)
UB DB U M' U' M' U' M' U' M U2 (9f*)

UF Flipped, Remaining M Edges Oriented

UF DF M2 U M U2 M' U M' U M' U2 M U (12,15)
UF DB M U' M' U2 M U M U M U2 M' U' (12,14)
UF UB M U M' U M' U2 M U2 M' U M' U (12,14)
DF UF F' L F' M2 F2 M F' L' F (9f*)
DF DB M F L F' M2 F2 M F' L' F' (10f*)
DF UB F' L F' M F2 M2 F' L' F (9f*)
DB UF B2 M' B L' B M' B2 M2 B L B (11f*)
DB DF F' L F' M2 F2 M F' L' F' M F2 (11f*)
DB UB F' L F' M F2 M2 F' L' F' M F2 (11f*)
UB UF M' B L' B M' B2 M2 B L B' (10f*)
UB DF F' L F M2 F2 M' F L' F (9f*)
UB DB F' L F M' F2 M2 F L' F (9f*)

Some of the algorithms in the last set of 12 work best by rotating the cube with x or x', but doesn't require a last x or x', as the cube will be solved at the end of this step. 

Looking at all the cases which use L, U, and M turns makes it tempting to mirror both steps ( solve LU, insert RU flipped in Step 1), so that these cases are in the RMU group of moves.

Step 1 should be solved intuitively. There are a few cases which can take up to 7 moves to solve optimally, but some can be solved in 3 moves.

In the event of LU and RU getting solved accidentally during CMLL, just orient the M layer and solve it in 2 steps.

In any case, this gives a true 2 look solve of the last 6 edges.


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