The 3x3 Example Solve Game with only half turns

[Renslay]

That's superb right there

I need help again cuz idk how to solve this case

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 L2 B2 R2 F2 D2 B2 U2 L2

 Moves 

L2 U2 L2 F2 U2

Next

I looked at your proposal. I don't know a direct solution, I'd do an L-pattern and then a 3-perm. If you chose the right algorithms, the cancellation is insane here!

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 L2 B2 R2 F2 D2 B2 U2 L2

 Moves 

L2 U2 L2 F2 U2 L2 B2 L2 (y x') B2 R2 U2 R2 B2

// original:
// L2 U2 L2 F2 U2 // your first part
// (L2 B2)3 // L-pattern
// yx' (R2 U2 R2 B2)2 // 3-perm

I originally inserted this as 3-perm:
yx' (L2 U2 L2 B2)2
But I realized I can use the mirrored version for a LOT of cancellation!

Is L2 B2 L2 (y x') B2 R2 U2 R2 B2 the shortest solution to this case? Honestly, I don't know. But I keep this in mind if I run into this exact pattern again!

 

[acrystal]

I looked at your proposal. I don't know a direct solution, I'd do an L-pattern and then a 3-perm. If you chose the right algorithms, the cancellation is insane here!

 Twizzle link 

 Setup 

B2 L2 B2 L2 B2 L2 B2 R2 F2 D2 B2 U2 L2

 Moves 

L2 U2 L2 F2 U2 L2 B2 L2 (y x') B2 R2 U2 R2 B2

// original:
// L2 U2 L2 F2 U2 // your first part
// (L2 B2)3 // L-pattern
// yx' (R2 U2 R2 B2)2 // 3-perm

I originally inserted this as 3-perm:
yx' (L2 U2 L2 B2)2
But I realized I can use the mirrored version for a LOT of cancellation!

Is L2 B2 L2 (y x') B2 R2 U2 R2 B2 the shortest solution to this case? Honestly, I don't know. But I keep this in mind if I run into this exact pattern again!

Oh, I thought you knew some alg but this works I guess as it is 8 moves. How could R2 U2 R2 F2 U2 be useful though?

 

[Renslay]

Oh, I thought you knew some alg but this works I guess as it is 8 moves. How could R2 U2 R2 F2 U2 be useful though?

Uhm, I don't understand. What does R2 U2 R2 F2 U2 do and where?

 

[acrystal]

Uhm, I don't understand. What does R2 U2 R2 F2 U2 do and where?

But I realized I can use the mirrored version for a LOT of cancellation!

 

[Renslay]

By mirrored version, I mean mirrored version of the 3-perm:
(L2 U2 L2 B2)2
versus:
(R2 U2 R2 B2)2
(mirrored across the yz plane)

Both do the same, but if the previous patterned ended up with R2, or even better, U2 R2, or even more... (considering the y x' move here), then the second is much better than the first.

 

[Renslay]

Next

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 F2 L2 U2 B2 R2 D2 R2

 Moves 

d2 L2 d2 L2 D2 L2 D2 B2 L2 B2 L2 D2 B2 D2 B2 D2

// original:
// d2 L2 E2 // corners
// (D2 L2)3 // L-pattern
// (L2 B2)3 // L-pattern
// (B2 D2)3 // L-pattern

Couldn't find any better.

Next: B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 

[acrystal]

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 F2 L2 U2 B2 R2 D2 R2

 Moves 

d2 L2 d2 L2 D2 L2 D2 B2 L2 B2 L2 D2 B2 D2 B2 D2

// original:
// d2 L2 E2 // corners
// (D2 L2)3 // L-pattern
// (L2 B2)3 // L-pattern
// (B2 D2)3 // L-pattern

Couldn't find any better.

Next: B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

OMG I JUST FOUND A 11-MOVE SOLUTION WITH LEGENDARY CANCELLATION

 Twizzle link 

 Setup 

B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 Moves 

Rw2 x y D2 L2 D2 F2 L2 F2 D2 L2 F2 R2

Next

 

[Renslay]

OMG I JUST FOUND A 11-MOVE SOLUTION WITH LEGENDARY CANCELLATION

 Twizzle link 

 Setup 

B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 Moves 

Rw2 x y D2 L2 D2 F2 L2 F2 D2 L2 F2 R2

Next

Hoooaaah, nice! Congrats! Care to explain / insert the non-cancelled solution?

 

[Renslay]

Next

Woaaaaah, I just found a 9-STM solution to this!

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

B2 E2 R2 B2 R2 U2 R2 B2 E2

I'm gonna put into spoiler how I did it, because it contains a trick I haven't used so far!

Spoiler: explanation

Original:

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

// original:
B2 U2 R2 // corners
(R2 E2)2 // H-pattern
(R2 U2 R2 B2)2 // 3-perm

Now with cancellation, but watch the E2 in the middle!

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

// original cancellation, but then I noticed I can remove the (E2) and put it at the end...
B2 u2 R2 (E2) R2 U2 R2 B2 R2 U2 R2 B2

// original:
// B2 U2 R2 // corners
// (R2 E2)2 // H-pattern
// (R2 U2 R2 B2)2 // 3-perm

 Twizzle link 

 Setup 

B2 L2 B2 L2 U2 D2 L2 F2 D2 L2 F2 L2 F2

 Moves 

// This is just moved the (E2) to the end:
B2 u2 R2 R2 U2 R2 B2 R2 U2 R2 B2 (E2)

This gives us the final cancellation...

Next: B2 L2 D2 B2 U2 L2 F2 R2 B2 D2 L2 D2 L2

 

[acrystal]

Hoooaaah, nice! Congrats! Care to explain / insert the non-cancelled solution?

 Twizzle link 

 Setup 

B2 L2 B2 U2 D2 F2 U2 L2 B2 D2 R2 B2 R2

 Moves 

M2 B2 R2 B2 // 223
x y D2 F2 D2 F2 D2 L2 D2 F2 L2 F2 D2 L2 F2 R2 // H-Perm

This uses your trick; M2 x y F2 -> Rw2 x y