CLL+1
Around 2010, Thom Barlow suggested the idea of a last layer method where the four corners are solved while also solving a single edge, then finish with the last three edges. However there wasn't a system for how to make it work. I provided a couple of ideas at the time, such as setting edges up using the M slice or creating a U layer pair while finishing the first two layers. None of the ideas were ideal. A few years later the idea was re-proposed by others. The idea then was to take advantage of edge phasing in COLL+1 to permute an edge and, in the case of CLL+1, Louis de Mendonça had the idea of having two algs per edge permutation case - one that orients edges a certain way and another that orients edges the opposite of the first to ensure the placed edge will be oriented correctly.
In 2020 I decided to take another look at the problem. I discovered a new kind of system where algorithms can be unioned to where one set of algorithms moves pieces a certain way and the other moves them in a different way, resulting in groups of algorithms that can solve multiple cases each. In the case of COLL+1 and taking the CP solved Sune 12 case set, only two algorithms are required for those 12 cases to solve an edge. One algorithm cycles edges in some direction and the other cycles them in a different way, resulting in a union where the algorithm solves an edge in some of the cases, the other algorithm solves an edge in some of the other cases, and both algorithms can be used in the remainder of cases. Then for CLL+1 to cover the edge's orientation, I had the same idea as Mendonça of having two algorithms each orienting all edges in an opposite way, though I learned of him having had the idea once he pointed it out to me when I showed my findings.
Because the solution of unioning algorithms is complex, developing CLL+1 took me 3 months and around 200 hours of work.
