What is CE F2L?
CE F2L is a method of solving the first two layers (F2L) on a Rubik's cube using the CFOP (Jessica Fridrich) method. It is not yet known if this method is slower or faster than CFOP, but, from my experience, it is slower.
It is called CE F2L because, instead of edges and then corners, you place corners in first, then edges. If you do not know F2L, you won't be able to solve this. F2L is advanced, so this is advanced as well.
This method has 3 steps:
Move F2L edges on upper face
What you first have to do is move all of the F2L edge pieces on the upper face (as seen above, with white face as base).
This is for compatibility: if the edges for F2L are on the bottom face and you have already implanted one of the corners, you cannot get that edge out without displacing a corner. (F2L edges are the edges that connect to the corners in F2L)
There is no algorithm for this, it is as simple as creating the cross in CFOP.
This step is pretty self explanatory. Perform F2L without base edges implanted.
As this method is a still a work in progress, there might be a problem. As I said in the previous step, if the edges are on the bottom, it will cause a displacement of a corner. Well, I am not sure if placing the edges on the top will help. Contact me on Steam or Twitter (@keterCSGO) if you have a situation where the edges were on top but ended on the bottom.
This step is the one step which is new, so I will go into it with detail.
For this step, you have to get each of the edges on the base face matched with it's center (completing the cross).
First, you must look for the white edges. There are 4 different states for the edges:
If the edge is solved, you don't have to do anything :)
If the edge is permuted, but not oriented, this is the algorithm:
M' D M D' M' D2 M
If the edge is on the side face, you implant it somewhat like you implement a corner in F2L. Move the piece to the side, middle slice down, put the piece in, and middle slice up.
D M' D' M
If the edge is on the bottom face, you middle slice down, rotate down twice, and middle slice up:
M' D2 M
If the edge is permuted, but in the wrong spot (it is in place of, or example, the green and white when it is the red and white), you simply move it down and away:
M' D M
Once you are done with that, all of the first two layers should be oriented and permuted