CLL+1

Thom Barlow started discussing the idea around 2010. However, there wasn't a system to make it work.

James Straughan provided a few ideas in response to Thom Barlow's request for a system.

In 2017, Louis de Mendonça mentioned an idea of phasing or unphasing the LL edges and using inverted EO algs depending on the EO case.

In May, 2020 James Straughan started looking into the CLL+1 problem again.

James Straughan found a new system and started developing the algorithms in July, 2020.

CLL+1 development was completed in September, 2020.

https://www.speedsolving.com/threads/cll-1-an-advanced-ll-method-complete-and-fully-generated.78631/#post-1394716
The system for solving any single edge during CLL is:
- Have two algorithms per CLL case. One algorithm cycles the four edges around in some way and will be able to correctly permute one of the four edges in some cases. The other algorithm cycles them around a different way and will be able to permute one of the four edges in some other cases. The directions in which the edges cycle in both algs will have an overlap where both algorithms can solve an edge in a few cases. This allows a user to only need to know two algorithms for the 12 possible edge permutations in order to correctly permute any single edge. Instead of learning all 12 algorithms and focusing on a specific edge every solve.
- As for edge orientation, each of the two algorithms will have a counterpart algorithm that flips edge orientation the opposite way of the original. So the edge that was correctly permuted can also be ensured to become correctly oriented. This makes two algorithms per COLL case for COLL+1 or four algorithms per CLL case for CLL+1. The edge orientation trick was independtly discovered by both Louis de Mendonça and James Straughan.
The algorithm overlapping, or union, system was developed into a concept of its own that can be used to solve other problems in method development. Check out the "Union Principle" page in the Techniques section for more information.