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. 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 that it was the way forward. Especially the idea of base EOLR (and not EOLRb) where the LR edges are set up to be either placed on the D layer 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 EOLR and is quite popular among Roux users.

My original post didn't call it EOLR. Instead I called it a "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 the community now calls it). It could be mentioned that Gilles Roux's website has a section on the LSE page about shortening the EO step, but that is only misoriented centers specifically with no mention of solving the LR edges during EO. Roux's site didn't include the idea of combining steps 4a and 4b into a single step. Roux's misoriented centers cases were there purely for making step 4a, the EO step only, as short as possible. EOLR can be done without the use of misoriented centers. Misoriented centers is just a technique that can be used to make EO and EOLR even shorter. Misoriented centers 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. In my version of EOLR I often left out the final M* of the final arrow EO because the LR edges will be either solved with that final M* or will need to be placed on the bottom then an AUF before using M2 to solve. My development also included all possible cases including AUFs, mirrors, and inverses, so there are more cases in the original tables 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.