MI2
This is the second method that I developed. The first version was developed in January 2010. The steps were EOLine -> All 8 Corners -> UF+UB edges -> L8E. I found the UF+UB edge step too restrictive, causing the movecount to be higher than it should. In October 2011, I found a better way of using EOLine to get to the domino reduction state and that is the method that is presented here.
Original site with the CLL variant (only the main page was preserved): https://web.archive.org/web/20110224050936/http://athefre.110mb.com/
Preserved post of the main variant presented on this page: https://www.speedsolving.com/threads/random-cubing-discussion.22862/post-650817
Step 1
Solve EOLine on the left. I decided to solve EOLine in this way to avoid a z rotation for the L8E step. RUD moves weren't very easy to perform on the cubes during the year that this method was developed. However, it still felt like the right way to go. Now that we have better cubes, having the first step oriented in this way proved to be a great choice.
Step 2
Build two 1x2x3s consisting only of U/D layer oriented pieces. One 1x2x3 is on the D layer and the other one is on the U layer. The blocks can contain a mix of U/D colors. This step is extremely efficient and very easy. It takes only a few moves per block. Some of these blocks can be planned and preserved during inspection. This means proceeding to the next step is very fast. For a more advanced, even more pseudo version, the first step of the method would involve placing two U/D edges at FL and BL then build the blocks with the corners oriented toward F/B.
Step 3
Orient the remaining four corners and move the U/D edges that are on the R layer to U/D. This step is exactly the same as the first step of NMLL. Very short algs. 41 cases.
Step 4
Permute the remaining eight corners. There are many ways that this can be done. A few examples:
Solve the D layer corners then the U layer corners.
Solve two corners at DL then permute the remaining corners.
Separate the correct corner colors to U/D then permute all.
Solve the three corners at DFL, DBL, and DBR then permute the remaining corners.
Step 5
Permute the remaining eight edges. The typical procedure is to solve two opposite edges on the D layer then permute the remaining six edges.
Step 2 + 3 Advancement
An idea for advancing the method is to solve an oriented 1x2x3 block on the bottom and an oriented 1x2x2 on the top. Then use an alg to orient all corners while placing the FR + BR edges.
Variants
1 (After Step 3)
Solve any 1x1x3 bar at DL.
Permute the remaining six corners.
Solve the last three L/R edges.
Permute the M Slice and perform any final adjustments.
Other edges can be solved in step 3 instead. Such as the three bottom layer edges then do EPLL. Or the DR edge and the UF+UB edges. The corner permutation algorithms can also be truncated to avoid initial R2s or S moves in the algs.
2 (After Step 3)
Solve any 1x1x3 bar at DL.
Solve a pair at DbR. (The bottom right, opposite of the 1x1x3)
Permute the last five corners.
Permute last six edges.
Additional Advancement Idea
There are many ways to make this method even faster. One that I'll mention here makes use of the A3 system. MI2 combines completely naturally with A3 to make MI2 a method that is easy to continue advancing.
EOLine on the D layer or L layer.
Form the two 1x2x3s consisting of blocks of pieces. The primary technique here would be to have each 1x2x3 consist of any two pairs and an edge. Other combinations are possible, however the two pair technique is a simple starting point.
Orient the remaining four corners and separate the remaining four edges. This is the same as step 3 in the original method.
Permute the pieces that were oriented in step 3 while permuting the pairs within the 1x2x3 blocks. This is the same as the permutation step of NMLL, which is only 15 cases. So for each type of pseudo 1x2x3, it would be easy to learn the corresponding algorithms.
What this creates is a method that converges with ZZ if A3 is applied. This advancement can be seen as MI2+A3 or it can be seen as ZZ+A3 with NMLL as the last layer method.