I've thought about this in regards to Waterman and also beginner's methods adapted from layer-by-layer that don't explicitly solve the cube layer by layer.
For instance, the method I used before my transition into CFOP was
1.) Cross
2.) Middle layer
3.) FL corners
4.) 4LLL
Even though it does, in a way, solve the cube one layer at a time, I wouldn't consider it a layer-by-layer method and rather a beginner's method. I think that "The Beginner's Method" has so many variants that instead of being grouped as one collective concept, all of the beginner's methods are under the term "beginner's methods". The layer-by-layer method in which one solves Cross, FL, 2nd layer, and LL in my opinion should be renamed "Traditional Layer-by-Layer" under the Layer-by-Layer methods umbrella. Just my two cents (and hopefully sense as well).
I've already gone about calling CLL for 3x3 3CLL; in my opinion, the different types of CLL and whatnot should be classified by colloquial names, as it has been done with PLL cases (Allan, Bert, and the like).
As far as 2-gen goes, I think the usage of the term '2-gen' should be lenient. Just as Lucas (or whoever) proved the cube was 2-gen (using two algorithms to solve the cube from any state), 2GLL uses only the R and U faces. Both are correct, and any feuding against the true definition is in my opinion unnecessary. Just don't be a dick about the whole thing like some people are being, saying "Well <R U R', D> is 2-gen!" Even though it is technically true, the kind of 2-gen a particular writing or whatever is talking about should be able to be figured out.




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