That's REALLY nice, but what exactly is your method? I mean, you said something about (r2f2r2) ux (r2f2r2) ux but I don't really get what that does or how you would do the setups. I can't see freestyle working for instance because setting everything up would be a nightmare and you seem to only be using u turns for setups. Also, how do you do centers?
I first solve corners (trivial), then centers with one of these algs:
1. (u2 r2)3
2. r u r u' r' u' r' u' r
3. front-back mirror of 2.
Watch how 2. breaks and restores the D corners. Permutation of U corners is of course restored because of 2-gen laws, and their orientation is luckily restored as well. To choose/setup these cases, I mainly look for where the U center is.
For edges, I use DF and DB as buffers and use 3-cycles involving those two edges plus an edge somewhere in the top two layers. I can use u-turns for setups, so four targest are sufficient:
Target LF: (r2 u2 r2 f)2
Target UF: (r2 u2 r2 f2)2
Target RF: (r2 u2 r2 f')2
Target LU: r' (u r2 f2 r2)2 r
They're short, repetitive and similar, which makes them easy to learn. Also, note how the f turn in the first three algs directly translates to where the edge is taken (from DF to LF/UF/RF with f/f2/f').
I also do them backwards, solving the piece at DB, which is very easy as well. Though mostly I solve repeatedly from DF and only go backwards if the DF place holds one of the two buffer pieces and DB doesn't. Since it will move that buffer piece to DB, I then go forwards again, i.e., from that point on I alternate between forwards and backwards. On the other hand... it doesn't really matter whether I solve from DF or DB, so I might alternate without being made so by a buffer piece, but just because I recognize it more easily or see that I don't need a setup by reversing the direction. So... my choices between DF and DB are somewhat chaotic.
Setups for remaining edges:
DL: r' f' r
LD: r' f' r u
RD: r f2 r'
DR: r f2 r' u'
Note the RD/DR setups rotate the buffer, but that just means cycling forwards instead of backwards and vice versa.
To flip non-buffer edges that were in the right place but wrong orientation from the start, I spend two cycles, one forwards and one backwards. Ending up with two flipped buffer pieces is almost always avoidable, if necessary I just spend two cycles for solving the last non-buffer edge instead of just one.
Once again thanks to Arnaud for bringing it up (as well as those who did so in the earlier discussions), Kare for his great ksolve with which I found the main alg, and Ville for scaring me and making me try harder.
Oh and making this video was a nightmare. Editing took me hours (need faster/better tools and more experience), and recording the explanation took about 25-27 attempts. I had some more text planned but couldn't talk fast enough to make it fit in the 41 seconds of scramble+inspect, and I also screwed up a lot. Still not 100% happy with the final version, I think I mumble "r u m" in the beginning and say "belief" instead of "believe" in the end, but it's got to be good enough. And when I finally finished last night around 2am - I didn't go to bed earlier because I wanted to publish it before - I found out that my internet connection was dead. Gah!