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Square-1 Lin L2DE+CP ("CMDLL") algorithms


Jun 13, 2019
This alg set solves the last 2 bottom edges as well as top layer CP, after the L/R half layers have been built in the Lin method and most of its variants. This leaves EPLL as the last step, making it a reasonably efficient solution to minimize parity damage without resorting to CSP. There are a total of 23 algs.

There are 5 such L2DE cases: 1-1 U-D swap, adj on U, opp on U, 3-cycle and D-D swap, multiplied by at most 6 CP cases each depending on symmetry just like on 3x3. Conventionally the U-D set has been considered the most basic, and all the other sets can be converted to it by one M2 (2 slices long). In each of the cases the 2 bottom edges are considered fixed while the 4 top edges are considered able to permute freely regardless of which layer they temporarily reside.

an optimal alg is ideally 6 slices long; since there exist algs of this length for the entire U-D set, on paper any eventual alg of 8 moves or more would be no more optimal than inserting 1 edge with M2 and then following up with the U-D alg of the same CP. There are only 3 such cases fortunately and they all also have a 7 move solution, which I have also included. The "opp on U" cases are similarly solved not much less optimally by inserting first (especially if the user also knows PLL) but once more there are only another 3 such cases.

Right swap 0,5/4,1/5,2/1,4/-4,-1/3,-3/0,1
Left swap 4,0/3,-3/0,3/0,-3/3,0/5,2/-3,1
Front swap 3,-1/0,-3/0,3/0,-3/3,0/-2,4/-4,0
Back swap 0,-1/3,-3/0,3/0,-3/3,0/-5,4/-1,0
Diag swap 1,0/3,2/3,0/3,3/3,0/2,3/6,1
No swap 1,0/3,0/3,0/-1,-1/-2,1/-4,-1/

Right swap -3,5/4,-2/0,3/0,-3/3,0/5,2/0,-5
Left swap -2,0/2,-4/-3,0/0,3/0,-3/1,4/5,0
Front swap 1,0/3,-3/2,5/4,1/5,2/0,3/3,1
Back swap 4,0/2,5/3,0/-3,0/0,3/-2,4/5,0
Diag swap 4,0/2,3/3,0/3,3/3,0/-3,2/-5,1/-1,0 [7|19]
No swap /0,-3/-3,0/0,-1/1,0/-1,0/3,1/0,3/

M2 Left swap 0,-1/1,-2/0,3/0,-3/3,0/-3,3/2,0
M2 Front swap 1,0/2,-4/3,0/-3,0/0,3/-3,0/3,1
M2 Diag swap -2,0/2,2/3,0/3,3/3,0/4,4/-1,0
Dswap Adj swap 0,-4/3,0/0,-3/3,0/4,-5/2,-4/3,-2
Dswap Diag swap 1,0/3,3/3,0/3,3/3,0/-4,2/-5,1/2,0 [7|19]

Right swap 0,-4/3,0/1,-2/-1,2/3,-3/3,0/6,-5
Left swap -5,-3/-3,0/-1,2/1,-2/-3,3/-3,0/-1,0
Front swap 4,0/3,0/3,-3/-1,2/1,-2/3,0/2,3
Back swap -3,-1/1,-2/0,3/0,-3/3,0/-4,2/6,1
Diag swap 4,0/2,3/0,-3/3,3/-3,0/-2,-3/-4,0
No swap -2,6/3,0/3,0/-1,-1/-2,1/-3,0/