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This thread is where I got started with FMC. It goes over insertions (both commutators and single moves) as well as many other helpful things. Also the wiki page for FMC techniques you may useful as well.

Thanks Julian!! But I still needing an example solve, may be premade, with an inserted move example...
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Also, I want to share my optimal PLLs with U, U', U2, or no AUF (A V PLL and a U at the end will have one extra move, I generated algs that don't have that extra move if its possible to delete the move)

Spoiler: 84 PLLs

Full list:

Without AUF:

H: R L U2 L' R' F' B' U2 B F (10 HTM)
Z: R L' U2 D2 R L' D R2 L2 U' F2 B2 (12 HTM)
U clockwise: F2 U L R' F2 R L' U F2 (9 HTM)
U counterclockwise: F2 U' L R' F2 R L' U' F2 (9 HTM)
J left: U2 r' U' r U2 l' U R' U' l2 (10 HTM)
J right: U2 l U l' U2 r U' L U r2 (10 HTM)
A clockwise: R' U R' D2 R U' R' D2 R2 (9 HTM)
A counterclockwise: R2 D2 R U R' D2 R U' R (9 HTM)
Na: F2 U2 R2 U F2 U2 F2 R2 U R2 U2 R2 F2 U (14 HTM)
Nb: F2 U2 L2 U' F2 U2 F2 L2 U' L2 U2 L2 F2 U' (14 HTM)
Y: R2 U' R2 F R' f' R' U R F' U' B U (13 HTM)
E: R2 U R2 U' F2 U R2 B2 D' L2 D B2 U' R2 (14 HTM)
F: R L' B2 L' D R' B2 L U' R2 L F2 R2 U (14 HTM)
T: R2 U R2 D' F2 L2 U' L2 D F2 U' (11 HTM)
V: R' U R' U' B' R' B2 U' B' U B' R B R (14 HTM)
Ra: R U2 R' U2 l U' l' U' R U l U R2 F (14 HTM)
Rb: R' U2 R U2 l' U l U R' U' R' F' R2 U' (14 HTM)
Ga: R2 u R' U R' U' R u' R2 F' U F (12 HTM)
Gb: R' U' R y R2 u R' U R U' R u' R2 (12 HTM)
Gc: L2 u' L U' L U L' u L2 F U' F' (12 HTM)
Gd: L U L' y' L2 u' L U' L' U L' u L2 (12 HTM)

With U' AUF:

L2 B2 F2 R2 D' L2 B2 F2 R2 (9f*) //H
D2 L' R F D2 U2 F' D2 U2 F L R' (12f*) //Z
F2 U' L R' F2 L' R U' F2 U' (10f*) //U counterclockwise
F2 U L R' F2 L' R U F2 U' (10f*) //U clockwise
L2 D' B2 D B2 U' B2 U B2 L2 (10f*) //J left
B U' F U2 B' U B U2 B' F' (10f*) //J right
R2 B2 R F R' B2 R F' R U' (10f*) //A counterclockwise
R' F R' B2 R F' R' B2 R2 U' (10f*) //A clockwise
R2 B2 U2 B2 U' B2 R2 U2 R2 U' B2 U2 R2 (13f*) //Na
F2 L2 U2 L2 U L2 F2 U2 F2 U L2 U2 F2 (13f*) //Nb
F2 U F2 U F2 U2 R B R' F2 R B' R' (13f*) //Y
R2 U B2 D' L2 D B2 R2 U' F2 U R2 U' R2 U' (15f*) //E
R2 B2 L R2 U' L F2 R' D L' F2 L' R (13f*) //F
R2 D' F2 U F2 R2 D B2 U' B2 (10f*) //T
B2 D' F2 U2 F2 R2 D' F2 U F2 D2 R2 U' B2 (14f*) //V
R U2 R' U B L' B' R B L B' U R' (13f*) //Ra
L U' B U L2 D2 R F R' D2 L U' B' (13f*) //Rb
R2 F2 D B2 D' B2 U B2 U' B2 F2 R2 U' (13f*) //Ga
B2 L2 R2 U L2 D' B2 D B2 U' R2 B2 U' (13f*) //Gb
L2 F2 D' B2 D B2 U' B2 U B2 F2 L2 U' (13f*) //Gc
B2 L2 R2 U' R2 D B2 D' B2 U L2 B2 U' (13f*) //Gd

With U AUF:

L2 B2 F2 R2 D L2 B2 F2 R2 (9f*) //H
F' L F L' R' F L R' F L' F' R2 (12f*) //Z
F2 U' L R' F2 L' R U' F2 U (10f*) //U counterclockwise
F2 U L R' F2 L' R U F2 U (10f*) //U clockwise
B' U F' U2 B U' B' U2 B F (10f*) //J left
L R U2 R' U' R U2 L' U R' (10f*) //J right
R2 B2 R F R' B2 R F' R U (10f*) //A clockwise
R' F R' B2 R F' R' B2 R2 U (10f*) //A counterclockwise
F2 R2 U2 R2 U' R2 F2 U2 F2 U' R2 U2 F2 (13f*) //Na
R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 (13f*) //Nb
R2 U' R2 U' R2 U2 F' L' F R2 F' L F (13f*) //Y
F2 U L2 U2 L2 F2 U L2 U L2 U2 F2 U' F2 U' (15f*) //E
R2 F2 L' R2 U L' B2 R D' L B2 L R' (13f*) //F
R2 D B2 U' B2 R2 D' F2 U F2 (10f*) //T
R2 U B2 D2 F2 L2 D F2 D B2 U2 R2 U' R2 (14f*) //V
F U' R B' R' F' R B R' U' F U2 F' (13f*) //Ra
R' U2 R U2 R' F R U R' U' R' F' R2 (13f*) //Rb
R2 F2 D B2 D' B2 U B2 U' B2 F2 R2 U (13f*) //Ga
B2 L2 R2 U L2 D' B2 D B2 U' R2 B2 U (13f*) //Gb
L2 F2 D' B2 D B2 U' B2 U B2 F2 L2 U (13f*) //Gc
B2 L2 R2 U' R2 D B2 D' B2 U L2 B2 U (13f*) //Gd

With U2 AUF:

L2 B2 F2 R2 D' L2 B2 F2 R2 U' (10f*) //H
L2 R2 D L2 R2 U L2 B2 L2 R2 F2 R2 (12f*) //Z
F2 U' L R' F2 L' R U' F2 U2 (10f*) //U counterclockwise
F2 U L R' F2 L' R U F2 U2 (10f*) //U clockwise
L2 D' B2 D B2 U' B2 U B2 L2 U' (11f*) //J left
B2 L2 U L2 D' B2 D B2 U' B2 U' (11f*) //J right
R2 B2 R F R' B2 R F' R U2 (10f*) //A counterclockwise
R' F R' B2 R F' R' B2 R2 U2 (10f*) //A clockwise
R2 B2 U2 B2 U' B2 R2 U2 R2 U' B2 U2 R2 U' (14f*) //Na
F2 R' F2 U2 R2 U2 R' F2 R2 U2 R' U2 F2 R2 (14f*) //Nb
F2 U F2 U F2 U2 R B R' F2 R B' R' U' (14f*) //Y
F2 U L2 U2 L2 F2 U L2 U L2 U2 F2 U' F2 (14f*) //E
B' F R' B2 D2 B2 F' R F' U2 B L' F (13f*) //F
R2 D' F2 U F2 R2 D B2 U' B2 U' (11f*) //T
R U R2 F R2 U' R' F2 L' U L F2 U2 F' (14f*) //V
L' U' L U2 R B2 L D L D' L2 B2 R' (13f*) //Ra
L' B2 R2 D' R D R B2 L U2 R U' R' (13f*) //Rb
F2 D B2 D L2 B D F' D2 B D' F' (12f*) //Ga
L D R' D2 L D' R' B2 D' R2 D' L2 (12f*) //Gb
F2 D' B2 D' R2 B' D' F D2 B' D F (12f*) //Gc
R' D' L D2 R' D L B2 D L2 D R2 (12f*) //Gd

Here are my FMC-Results from Euros, 2nd place, first official mean and official single pb

Spoiler: 31 Moves

Scramble: F L2 D2 B’ L2 B U2 L2 B F2 U’ L’ D U2 F’ U’ R F2 U’ R’
Premove: F’
L’ U2 B2 U’ - 2x2x2 [4/4]
F R2 D2 R’ D’ R’ D2 F’ D F’ - F2L-1 [10/14]
D2 R2 D’ R’ F’ R2 F - Finish [7-1/20] Premove cancels with the last Move

L4C:
L’ U2 B2 . U’ F R2 D2 R’ D’ R’ D2 F’ D F’ D2 R2 D’ R’ F’ R2
. = F D F’ U’ : F D’ F’ U [8-4/24]
: = U’ L2 U R U’ L2 U R’ [8-1/31] - bad luck with the insertion compared to the first one

L’ U2 B2 F D F’ U2 L2 U R U’ L2 U R’ F D’ R2 D2 R’ D’ R’ D2 F’ D F’ D2 R2 D’ R’ F’ R2 - 31 Moves

Spoiler: 25 Moves

Scramble: L2 U2 B2 L2 F’ U2 L2 D2 L2 B’ F D’ R D2 F’ L’ F’ L2 D F’ L
inverser: L’ F D’ L2 F L F D2 R’ D F’ B L2 D2 L2 U2 F L2 B2 U2 L2

Pre: F'
F U2 L B’ D2
L2 F2 U’ F2
R B R’ U B’ U B U

L3C:
. F U2 L B’ D2 L2 F2 U’ F2 R B R’ U B’ U B U F'
. = U B U’ F2 U B’ U’ F2 [8-1/25] - again, bad luck with insertions I really hoped for a better results, but no..

U B U’ F2 U B’ U’ F' U2 L B’ D2 L2 F2 U’ F2 R B R’ U B’ U B U F’ - 25 Moves

Spoiler: 29 Moves

Scramble: F R2 B’ U2 F2 R’ F’ U2 B2 L’ D’ L’ U2 B’ U’ R'
inverser: R U B U2 L D L B2 U2 F R F2 U2 B R2 F’

R’ D’ F’ L’ B2 D F’ R’ F’ U F R’ B’ R2 B R’
5 Corners, 2 two of them twisted in 16

R’ D’ F’ L’ B2 D F’ - 2x2x2 + 1x2x2 [7/7]
R’ F’ U F - XX-Cross [4/11]
R’ B’ R2 B R’ - Finish [5/16]

L5C, ein pure twist:
R’ D’ F’ L’ : B2 D F’ R’ . F’ U F R’ B’ R2 B _ R’
. = R’ B2 R F’ R’ B2 R F [8-3/21] - solves the l3c, not 2 twisted remain
: = D F’ D’ B2 D F D’ B2 [8-6/23]
_ = B’ D B U’ B’ D’ B U [8-2/29]

R’ D’ F’ L’ D F’ D’ B2 D R2 B2 R F’ R’ B2 R U F R’ B’ R2 D B U’ B’ D’ B U R’ - 29 Moves

Well, it used to be at Per's FMC site (mustcube.net) but that's been down for at least a half year, currently we have David Adams's FMC site here. The FMC cube companion has more or less been replaced by alg.cubing.net

My site has moved to http://fmcsolves.cubing.net/
I renew my invite to good FMCers to post some solves on my blog.
Contact me, I'll give you an account and a few guidelines for posting solves

EDIT: to avoid double-posting, here is another CF solution: alg.cubing.net. 35 HTM isn't great, but I thought I could share anyway

L2 R2 F' R2 F D2 R2 D2 U2 B2 D B D U R2 D2 L' D B D'

x' y' U R2 U' D L2 R2 D2 U' L F' L' U R' F R U F R' F' R U L U L2 B R' D R U2 R' D' R U2 L B' (35)

8 move insertion with no cancels is before the last 2 moves
U L U L2 B * L B'
Solution without insertion;
x' y' U R2 U' D L2 R2 D2 U' L F' L' U R' F R U F R' F' R U L U L2 B L B' (27)

I spent about 40 minutes without touching a pen, trying to blockbuild to PLL skip or something, probably did 80+ with no PLL skip or 3 corner type thing. Found a 5 move 2x2 that I messed around with a lot.

Realised I had nothing written down with 20 mins left, found this 27 move CFOPy skeleton and found an insertion with no cancels with about a minute and wrote it down quickly. I realise rotations are bad, I should've done a proper hour-long solution trying inverse scramble and writing no rotations but wasted too much time.

Any insertions I missed? This tied my comp PB so any cancelations would've been nice.

Finding this for over an hour, as the result is 32 moves.

apply on normal: B L D (2x2x1 block)
switch to inverse: D' L' B' (In. SC) F' L2 (2x2x2 block)
U R (another block)
R U R' (CE pair)
B2 D' R' D R2 B R' (insert blocks)
F R' F' R (two layers)
R B2 L' B' L B' R' (OLL)
R B' R F2 R' B R F2 R2 (PLL)

scramble: R2 F2 R D' U2 L2 R' F L R2 U2 L D' U2 F L2 D' B2 L D' L2 D U' R D2

D2 R U B L' D' L' B
R U2 R2 F2
U' F R2 F' U R
on inverse:
U2 F' U' F
F R U R' U' F' U2

skeleton: D2 * R U B L' D' L' B R U2 R2 F2 U' F R2 F' U R U2 F U R U' R' F2 U F U2 (28)
* D2 U2 L' D L D2 U2 R' D' R
solution: U2 L' D L D2 U2 R' D' R2 U B L' D' L' B R U2 R2 F2 U' F R2 F' U R U2 F U R U' R' F2 U F U2 (35)

when i put my skeleton into IF, it gives this (saying 36 moves is optimal for my skeleton):

Spoiler

R2 F2 R D' U2 L2 R' F L R2 U2 L D' U2 F L2 D' B2 L D' L2 D U' R D2
Your Skeleton
D2 R U B L' D' L' B R U2 R2 F2 U' F R2 F' U R U2 F U R U' R' F2 U F U2

1 edge 3-cycle(s) insertion(s) needed

D2 R U B L' D' L' B R U2 R2 F2 U' F R2 F' U R U2 F U [@1] R U' R' F2 U F U2
Insert at @1: D2 R2 B R2 D2 L2 F L2
Fewest moves: 36. 0 moves cancelled
The final solution: D2 R U B L' D' L' B R U2 R2 F2 U' F R2 F' U R U2 F U D2 R2 B R2 D2 L2 F L2 R U' R' F2 U F U2

etc.

why wasn't IF able to find the same 35-move solution?

Well, that means that IF doesn't always give optimal results... Or that you are insertion god

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The commutator [F L' D2 L F, U2] can be adapted (changing the first F move to F2orperforming the rotations "y2 z" and then change the first F to F2) to solve this cases:
[CUBE]case=U R2 U' B R2 D' R2 D B2 U' B U R2&view=plan[/CUBE]
[CUBE]case=F U' R2 U R2 U F U' F2 D R2 D' R2&view=plan[/CUBE]

But can it be adapted to solve this:
[CUBE]case=U' B U' F U2 B2 D' R2 U D F' U' B&view=plan[/CUBE]
?

I don't actually do FMC, but I've heard twisted corners are very bad cases to get and it's best to avoid them. I would do sune+U perm given no other choice, but you'd have to ask an FMCer, because they would actually know what they're talking about.

I don't actually do FMC, but I've heard twisted corners are very bad cases to get and it's best to avoid them. I would do sune+U perm given no other choice, but you'd have to ask an FMCer, because they would actually know what they're talking about.

Well, that's clearly false. twisted corners give the best cancelations as you have the most freedom during the first insertion. 2 twisted corners is surely the best "2 insertions" case. However, of course it is nicer in general to end up with 3 permuted corners instead of 3 twisted corners, as the former requires only one insertion.

In the end, it's always a matter your skeleton's length.