EOLR

In 2012 I developed every LSE case for orienting the edges and placing the UL+UR edges. It produces the shortest solution to an EO arrow case where the user then either places UL+UR at DF+DB or solves UL+UR with M or M'. It also included around half of all possible EOLRb cases including the possible AUFs. This was the first ever development of EOLR. This development included both EOLR and EOLRb. All 285 included solutions were also found by hand with no computer assistance.

The development wasn't very well received at the time because most Roux users didn't have a big focus on this aspect of the Roux method. I also didn't explain it well enough. Although EOLR seems like an obvious idea now and it may seem obvious that it is the definitive improvement over 3 step LSE, it wasn't so obvious during those years. Especially the idea of setting up the L/R edges to be either placed on D or perfectly slotted when the AUF is right. There was hesitation and doubt that learning and trying to recognize a lot of cases in LSE would be viable. But I had been experimenting with it for years and saw how my LSE times and solutions were much better compared to what they were without EOLR. Nowadays solving 4a + 4b is known as EOLR and is quite popular among Roux users. It has also branched off into a couple of variants - the same way as in my original post.

My original 4a+4b post had a thread title that didn't clearly describe the system. It was titled "Misoriented Centers Table" just because it sometimes takes advantage of misoriented centers while solving EO and the LR edges (just as more recent EOLR documents do). But it should have just been called "Roux 4a+4b" (or EOLR as it is now called). It could be mentioned that Gilles Roux's website has a section on the LSE page about shortening the EO step. Although EOLR (combining 4a+4b) and misoriented centers are kind of linked if you want the shortest solutions, EOLR and misoriented centers are still two separate concepts and that section didn't include the idea of EOLR nor any developments for EOLR. The intent there was to describe the technique of using any center orientation to solve just the EO step in as few moves as possible - misoriented centers. EOLR can be done without the use of misoriented centers. Misoriented centers is a technique that can be used to make EOLR even shorter. It is another example of the use of pseudo solving and in that way is similar to the move count reduction provided by non-matching blocks (pseudo) vs normal blocks.

EOLR is when the edges are oriented and the LR edges are placed on the bottom layer. Except in my version of EOLR I allowed for three possible end states. Either having LR be solved, placed on the bottom layer, or left at the arrow EO state one move away from LR being solved. Doing this allows for the shortest possible solutions per EO case and each of the four AUFs before performing EO. It also gives the user a bit of additional freedom after the step to manipulate 4c. As a result of accounting for the possible AUFs and case mirrors, there are more cases in the original tables in the post than modern EOLR.

EOLRb was also included in the original post. EOLRb is when the edges are oriented and the LR edges are solved every time. 285 of the possible cases (or around half) including mirrors and inverses were developed at the time. The intention to develop the other half can be seen in a later post in the topic where I mentioned that it was LR neutral at that time (treating LR as the same colors). Distinguishing LR and solving them correctly means EOLRb and LR neutral naturally leads to EOLR. I left for the military around that time so the other half of EOLRb wasn't added.