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Nothing new. Just cool executions for [U' : M2 , R] and its inverse [R , U' : M2]. Now,

A = U' Rw M' R' U (= U' M2 U). This can be done in two "clicks": (U' Rw) (M' R' U).
B = R U' Rw M' R' U R' (= R U' M2 U R'). This can also be done in two "clicks": (R U' Rw) (M' R' U R').

Notice that [U' : M2 , R] = A B and [R, U' : M2] = B A. Very fun to execute

J perm: Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' Rw' F Rw2 U' Rw' U'
T perm: Rw' U' R U r U' R' U R2 U R' U' r U r' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'

T perm: Rw' U' R U r U' R' U R2 U R' U' r U r' F' Rw U Rw' U' Rw' F Rw2 U' Rw' U'
J perm: Rw' U' R U r U' R' U R2 U R' U' r U r' U' Rw' F Rw2 U' Rw' U' Rw U Rw' F'

Normal M2 parity involves swapping UB DF and UBL UBR. I believe that most people do F2 y' T perm y F2.
However, has anybody thought of using U Lw R U2 Rw' U' Rw U2 Lw' U R' U2?
Seems much much faster to me

Wow, noone has found any algs since I last posted a bld parity. Anyway, I had a random thought today about bld parity with edge flip of DF UB. I think maybe most people do something like (F U L') T Perm (L U' F'). Or even sillier (F2 y T Perm y' F2)(F2 flip UF and UB F2).
Enough blurb, here's the alg I think I would be switching to if I still did bld: U F2 Lw' U' R U2 L' U R' U' Rw R Uw'
I know it's pretty crazy, but I can do it fast. I'll make video to show how to execute these random parities soon

Wow, noone has found any algs since I last posted a bld parity. Anyway, I had a random thought today about bld parity with edge flip of DF UB. I think maybe most people do something like (F U L') T Perm (L U' F'). Or even sillier (F2 y T Perm y' F2)(F2 flip UF and UB F2).
Enough blurb, here's the alg I think I would be switching to if I still did bld: U F2 Lw' U' R U2 L' U R' U' Rw R Uw'
I know it's pretty crazy, but I can do it fast. I'll make video to show how to execute these random parities soon

Yes I thought there might be a T Perm edge flip alg out there somewhere, but that still requires F2 setup and a rotation/extra AUFs so I'm not yet sure which one is better

My alg is just a U R' into a J perm (R U2 R' U' R U2 L' U R' U' L'). Different J perm because it's the one I normally use. I didn't think of doing U Rw setup to avoid a slightly awkward rotation so thanks for that.

I would use y L2 (R Lw U' R' U Lw' F' U' F R U R' U') L2 y' (adapted alg from Aron's 22LL page).
I don't use it because my buffer is UF and because I solve parities with OP remembering swapped egdes in a wrong way.

Can someone create for me a shorter / more comfortable solution to this?
M2 U' M2 F R U' R' U' R U R' F' R U R' U' R' F R F' M2 U
or in short: M2 U' M2 Y-perm M2 U