Hi guys, I've been tinkering with a 4x4 method lately that I think is more efficient than K4 and comparable to Yau. Substeps are as follows (Haven't got a fancy name or anything, I've just been calling it CFCE):
1. Cross: Centers + cross dedges, identical to Yau
2. F3L. Two substeps:
2a. Using F2L techniques, solve the 1st layer + at least 1 E wing piece for each F3L slot
2b. Using K4 techniques, complete F3L.
3. CLL
4. ELL: Solve last 8 wing pieces, identical to K4
This must be more efficient than K4:
Cross will take slightly less moves than Layer;
During 2a, each "F2L pair" takes moves less than or equal to moves needed to insert a wing during K4 F2L; and
2b, CLL, ELL are same as in K4.
Efficiency is comparable to Yau:
CFCE contains: cross, 3x3 style F2L, half of K4 F3L, K4 LL
Yau contains: cross, 3-2-3, 3x3 style F2L, CFOP LL, 1/2 parities
Since both contain cross and 3x3 style F2L, we only need to compare movecounts of (half k4 F2L + k4 LL) vs (3-2-3 + CFOP LL + 1/2 parities).
CFCE: 4 wing pieces * 8 moves per wing + 9 moves CLL + 3 ELL comms * ~10 moves per comm = 71 moves
Yau: ~33 moves 3-2-3 (from some counting on cubesolv.es) + 10 OLL + 13 PLL + 1/2 * (7 PLL parity + 17 OLL parity) = 68 moves
On paper, F3L lookahead is much easier than 3-2-3 lookahead (in F3L, you're looking for any E wing, just like in F2L, while in 3-2-3 you look for specific wing pieces based on whatever's currently in the E slice). I think this more than compensates for the small increase in movecount, especially if there exist ways to bring down F3L movecount further with special tricks.
