L7E

This is an L7E method which is developed to work for Waterman, 42, SSRC, and any other method which has a free M slice and edges remaining unsolved on the left and right side. It is a sort of extension of the popular Roux LSE method. In LSE the basic version is that edges are oriented while positioning an L/R edge (or occasionally both). Then the remaining L/R edge is solved. Finally the M slice is permuted. In this L7E method, the first step is the same as LSE. Use iterative EO to orient the edges while positioning an edge. Then in the second step the remaining two L/R edges are solved and finally the M slice is permuted.

Iterative EO

In this step, iterative EO is used to orient all seven edges. Determine your edge orientation case, perform the algorithm, and repeat that process until all of the edges are oriented. During this edge orientation process an L/R edge can be positioned. This is easy because, just as in LSE, there will always be at least two L/R edges within the U and M layers. Surprisingly, this is the first development of iterative EO for L7E. I suppose it does seem during initial thoughts that it would be complex because there are two empty edge slots on the right side and the question arises of when to use slice moves and when to use wide moves. But it turns out that it is very simple. One of the empty edge slots will be at FR or BR. If the edge there is oriented, then the iterative EO is exactly the same as in LSE. If it is misoriented, then slice turns or wide turns can be used to set up to an arrow EO case (of which there are a few types).

View algorithms

LR

Next the remaining L/R edges are solved. This can be performed intuitively. But it is best to learn the best or most ergonomic solutions for each case. During the previous EO step, an edge should have been placed. This edge will be either in its correct slot or in another slot. Algorithms are provided for a couple of situations. There are 30 algorithms each, for a total of 60 counting the solved state.

This step also works when UF/UB edges have been solved during EO. More can be developed for other edge situations. Especially useful would be cases where an edge wasn't slotted during EO and when it makes more sense in the current corner situation to solve the UF+UB edges instead.

View algorithms

M Slice

In the final step, permute the M slice edges. These are the same cases as in Roux LSE and there are only a few. 3-cycles, bars, and dots.

L7EOLR

For LSE there is EOLR for further reducing the movecount. Two types of EOLR exist. One, simply called EOLR, which orients the edges and places the two LR edges at DF+DB. And then there is EOLRb which orients the edges and solves the LR edges. The same can be done here in L7E. An interesting thing is that in L7E there will always be at least two LR edges within the U layer and M slice. Sometimes all three LR edges will be there. So that gives the user options during EOLR to decide which two edges to place at DF+DB or solve. When the empty R layer edge slot is oriented it is the same number of EOLR cases as in LSE. When the edge slot is misoriented, it will be pretty much the same as well. Something that should be analyzed is how much of a reduction in movecount EOLR would provide over the primary steps of EO+edge > LR edges > M slice permutation.

The way EOLR should work here is likely the below steps:

For the first step, there are a few interesting things to consider. The sequence of moves doesn't necessarily have to place the last two L/R edges on the D layer. It can stop at the point where they are above and below each other at UF+DF or UB+DB. This can allow for useful cancellations. Also, the edge that is solved doesn't really have to be an L/R edge. It can be any U layer edge and the initial transformation state will be turned into a different one temporarily while continuing with placing EO + the relative L/R edges. Finally, EOFB works here just as it does in Roux.