Less is More
You will only need one algorithm: R' F R F'. Let's call this algorithm CA.
The four steps
- 1. First step is to intuitively build the cross on the bottom layer.
- 2. Secondly build the cross on the side faces, first moving edges pieces in the correct spot in the second layer (use CA for that), living one edge unsolved in the second layer.
- 3. Third step is to build a T shape on the top, with the closest edge with the wrong colour, then change the three pieces, solving all the crosses.
- 4. Fourth step is to exchange corners. To do that, find suitable corners to move to the bottom layer: one of the faces in the left or right side must match the bottom colour, and the remaining face should match the colour of the centre piece (if not, turn upper layer until it does). Now, do the CA. After that, "save" the correctly placed corner setting a wrong placed corner (already on the bottom layer) in its place, and then reverse the algorithm (CA'), so the other pieces come back to its places. After that, bring the corner back to the right place. Do that until you solve all the corners. And that's it!
Things to be aware before you start: (a) The centre pieces are a rigid cross, and they don't move in relation to each other; (b) The algorithm CA works by firstly overlapping to movements, and then doing the reverse of each one. The overlapping makes two pieces to rotate 90 degrees downwards, and only affect seven adjacent pieces (three corner, and three edges).
The method is a variation, modification and simplification of the Philip Marshall's method, using its steps, but mixing the use of only one very known algorithm with intuitive notions of commutators and conjugators. I would like to thanks those who created the following tutorials, that were fundamental for me to understand and elaborate my method. The references are listed below.
Video About this method: https://www.youtube.com/watch?v=IBkka-fhgg4&list=UU--QBHLCtx7kgiukctIjSUQ
About overlap and commutators: https://www.youtube.com/watch?v=Vw6dSkYk7G4
About Commutators and conjugators: https://www.youtube.com/watch?v=54SGrZbLcoE