Lately I've been looking at a sort of Roux-CFOP hybrid. I've been trying to learn Roux lately, and realized that, though there is a lot of freedom in blockbuilding, you almost always end SB by inserting an F2L style pair; this method tries to make use of that. Here are the substeps in outline:
1) FB
2) SB (up to last pair)
3) Place last slot while permuting corners
4a) Use <M,U> to orient D edges
4b) Use a modified OLL alg set (doesn't affect corner permutation) to orient LL
5) LSE, with edges oriented from step 4
The idea here is that, since making the last pair involves mostly M slice moves, which doesn't disturb corner permutation, I could potentially identify the CP case ahead of time while placing the last slot, and then the OLL would allow me to skip the EO recognition/halfstep. Further, OLL has easier recognition than CMLL imo, so the transition into step 4 would be smoother (though the CP recognition for step 3 could be a bit of a pain, so it's hard to say how this would pan out in practice).
Step 4a (orienting D edges) on average takes only 2-3 moves, and can be affected during the placement of the last pair, so I don't think it'd take much time, and about half of the standard OLL algs don't affect corner permutation anyway (i.e. variants on sune/asune & doublesexy), so step 4b should not be too bad.
I also learned yesterday that CP isn't affected by <R,U>, so I'm wondering if it'd be possible to identify the corner case while building the SB, eliminating some of the delay in recognizing the proper CP case when placing last slot.
I've made a
webpage that explains the method in detail with algs that I've generated and diagrams explaining them.
What do you guys think?