Speedsolving Posts: Almost-2gen LL Algs

From http://www.speedsolving.com/forum/showthread.php?18539 (January 2010):

From any ZBLL we can easily get to PLL using only 2gen moves. All PLLs are a U, Z, or H perm away from either solved, R perm, or Y perm. Therefore, if we can do R and Y perm with at most 2 D-layer moves, we can do any ZBLL with at most 2 D-layer moves.

So, here is an R perm with exactly 2 D-layer moves:
R U2 R D R' U R D' R' U' R' U R U R' U
And here is a Y perm (but not an efficient one):
R' U' D (R' U' R U)3 D' U R (R U R' U R U2 R')2 U'

I imagine these algs could be very useful for OH - everyone loves 2gen moves, and keeping D turns to a minimum is very helpful. Unfortunately, I don't know of any way to generate optimal algs of this type. Does anyone have an idea?

P.S. You can also do every ZBLL with and at most two F moves, although it's less useful IMO. You can prove this with the T perm and this Y perm:
F (R U R' U')3 F' U (R U R' U R U2 R')2 U2 

From http://www.speedsolving.com/forum/showthread.php?708&p=680961#post680961 (December 2011):

Dumping some optimal 2-F-move PLLs (there are probably a few optimal ones I missed but the optimal lengths should be accurate):

A-perm a
HTM-optimal: 11f
 R U' R F2 R' U R' U' R2 F2 R2

QTM-optimal: 15q
 R U' R F2 R' U R' U' R2 F2 R2

A-perm a
HTM-optimal: 11f
 R2 F2 R2 U R U' R F2 R' U R'

QTM-optimal: 15q
 R2 F2 R2 U R U' R F2 R' U R'
 

E-perm

HTM-optimal: 18f
 R' U2 R U' F' R' U R' U2 R U R' U R2 F R' U' R
 R' U R F' R2 U' R U' R' U2 R U' R F U R' U2 R
 R U R' U R' F U' R2 U' R2 U2 R' U' R F' R' U R2
 R2 U F' U R' U' R U R' U' R U R' U' R F U' R2
 R2 U F' R' U R U' R' U R U' R' U R U' F U' R2
 R2 U' R F R' U R U2 R2 U R2 U F' R U' R U' R'
 R2 U2 F' U' R' U R U' R' U R U' R' U R F U2 R2
 R2 U2 F' R' U' R U R' U' R U R' U' R U F U2 R2
 F U R2 U' R U R' U R2 U' R' U R' U' R U' R F'
 F U' R U' R U R' U R U2 R' U R' U' R U2 R' F'
 F U' R U' R' U2 R U' R' U R' U2 R U R' U R F'
 F U' R' U R' U' R2 U R' U R U' R2 U R U' R F'
 F R U2 R' U R U' R U2 R' U' R U' R' U R' U F'
 F R' U R' U R U' R U R2 U' R U' R' U R2 U' F'
 F R' U R' U' R2 U R' U' R U' R2 U R U' R U F'
 F R' U' R U' R' U2 R U' R U R' U2 R U R' U F'

QTM-optimal: 20q
 R2 U F' U R' U' R U R' U' R U R' U' R F U' R2
 R2 U F' R' U R U' R' U R U' R' U R U' F U' R2
 F U R2 U' R U R' U R2 U' R' U R' U' R U' R F'
 F U' R U' R U R' U R U2 R' U R' U' R U2 R' F'
 F U' R U' R' U2 R U' R' U R' U2 R U R' U R F'
 F U' R' U R' U' R2 U R' U R U' R2 U R U' R F'
 F R U2 R' U R U' R U2 R' U' R U' R' U R' U F'
 F R' U R' U R U' R U R2 U' R U' R' U R2 U' F'
 F R' U R' U' R2 U R' U' R U' R2 U R U' R U F'
 F R' U' R U' R' U2 R U' R U R' U2 R U R' U F'
 

F-perm
HTM-optimal: 15f
 R2 U R2 U2 F2 U R2 U2 R2 U R2 U' R2 U2 F2
 R2 U R2 U' R2 U2 R2 U' F2 U2 R2 U' R2 U' F2
 F2 U R2 U R2 U2 F2 U R2 U2 R2 U R2 U' R2
 F2 U2 R2 U R2 U' R2 U2 R2 U' F2 U2 R2 U' R2
 R2 U' F2 U2 R2 U' R2 U2 R2 U R2 U F2 U2 R2
 R2 U2 F2 U' R2 U' R2 U2 R2 U R2 U2 F2 U R2

QTM-optimal: 19q
 R U R' U' R' U R U F' U R' U R U2 F R U' R'
 R U R' F' U2 R' U' R U' F U' R' U' R U R U' R'
 R U R U F' U' R U R' U' R' U2 F U' R' U2 R'
 R U2 R U F' U2 R U R U' R' U F U' R' U' R'
 R' U' R U' R' U R U R2 F' R U R U' R' F U R
 R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R
 

G-perm a
HTM-optimal: 15f
 F2 U R U2 R' U' R' U2 R2 U R' F2 R' U R
 R' U' F2 U R U2 R U2 R' U F2 U2 R U' R'

QTM-optimal: 18q
 R U R' U' R' U F R U R U' R' F' U R' U2 R
 

G-perm b
HTM-optimal: 15f
 R' U' R F2 R U' R2 U2 R U R U2 R' U' F2
 R U R' U2 F2 U' R U2 R' U2 R' U' F2 U R

QTM-optimal: 18q
 R' U2 R U' F R U R' U' R' F' U' R U R U' R'
 

G-perm c

HTM-optimal: 14f
 R2 U2 R2 F2 U' R2 U R2 U F2 U2 R2 U' R2

QTM-optimal: 17q
 R2 U' R U' R U R' U R' F' R' U R U' F R'
 

G-perm d
HTM-optimal: 14f
 R2 U R2 U2 F2 U' R2 U' R2 U F2 R2 U2 R2

QTM-optimal: 17q
 R F' U R' U' R F R U' R U' R' U R' U R2
 

J-perm a
HTM-optimal: 13f
 R' F R' U' R2 U' R2 U R' F' R U R2
 R2 U' R' F R U' R2 U R2 U R F' R

QTM-optimal: 16q
 R' F R' U' R2 U' R2 U R' F' R U R2
 R2 U' R' F R U' R2 U R2 U R F' R
 F R' U R U' F' U R' U2 R U' R' U2 R
 R' U2 R U R' U2 R U' F U R' U' R F'
 R' U' R U F R U' R' U' R' U R2 U R' F'
 R' U' R U' R' U F U R' U' R F' R' U R2
 R2 U' R F R' U R U' F' U' R U R' U R
 F R U' R2 U' R U R U R' F' U' R' U R
 

J-perm b
HTM-optimal: 11f
 R U' F U' R' U' R U F' U2 R'
 R U2 F U' R' U R U F' U R'

QTM-optimal: 12q
 R U' F U' R' U' R U F' U2 R'
 R U2 F U' R' U R U F' U R'
 

N-perm a
HTM-optimal: 15f
 R2 U R2 U' R2 U' F2 U' R2 U R2 U F2 U2 R2
 R2 U2 F2 U' R2 U' R2 U F2 U R2 U R2 U' R2

QTM-optimal: 21q
 R U2 R2 U' R2 F' R U R' U' R' F R' U R U2 R'
 R U2 R' U' R F' R U R U' R' F R2 U R2 U2 R'
 R U R' U R U' F U' R' U' R U F' U2 R' U2 R U' R'
 R U R' U2 R U2 F U' R' U R U F' U R' U' R U' R'
 

N-perm b
HTM-optimal: 15f
 R2 U F2 U2 R2 U R2 U2 R2 U' R2 U2 F2 U' R2
 R2 U' R2 U2 F2 U' R2 U2 R2 U F2 U2 R2 U R2

QTM-optimal: 23q?
 R U' R' U R' U2 R2 U R2 F2 U R U R U' R' U' F2
 F2 U R U R' U' R' U' F2 R2 U' R2 U2 R U' R U R'
 R' U2 R' U' R2 U F' U' R U R' U' R2 U2 R F R' U R
 R' U2 F U R2 U2 R' U' R U R' F' R U2 R' U' R' U R
 R' U' R U R U2 R' F R U' R' U R U2 R2 U' F' U2 R
 R' U' R F' R' U2 R2 U R U' R' U F U' R2 U R U2 R
 

R-perm a
HTM-optimal: 13f
 R2 F2 U R U R' U' R' U' F2 R' U R'
 R U' R F2 U R U R U' R' U' F2 R2

QTM-optimal: 16q
 R2 F2 U R U R' U' R' U' F2 R' U R'
 R U' R F2 U R U R U' R' U' F2 R2
 

R-perm b

HTM-optimal: 13f
 R2 F R U R U' R' F' R U2 R' U2 R
 R' U2 R U2 R' F R U R' U' R' F' R2

QTM-optimal: 16q
 R2 F R U R U' R' F' R U2 R' U2 R
 R' U2 R U2 R' F R U R' U' R' F' R2
 

T-perm

HTM-optimal: 14f
 R U R' U' R' F R2 U' R' U' R U R' F'
 F R U' R' U R U R2 F' R U R U' R'

QTM-optimal: 15q
 R U R' U' R' F R2 U' R' U' R U R' F'
 F R U' R' U R U R2 F' R U R U' R'
 

V-perm
HTM-optimal: 15f
 R2 U2 R2 U R2 U2 F2 U R2 U R2 U2 F2 U' R2
 R2 U2 R2 U' F2 U2 R2 U' R2 U' F2 U2 R2 U R2
 R2 U F2 U2 R2 U' R2 U' F2 U2 R2 U' R2 U2 R2
 R2 U' R2 U2 F2 U R2 U R2 U2 F2 U R2 U2 R2

QTM-optimal: 19q
 R U' R' U R F R' U' R2 U R U' R U R2 F' R'
 R F R2 U' R' U R' U' R2 U R F' R' U' R U R'
 

Y-perm

HTM-optimal: 14f
 R2 U' R2 U F2 U' R2 U' R2 U F2 R2 U R2
 R2 U' R2 F2 U' R2 U R2 U F2 U' R2 U R2

QTM-optimal: 19q
 R2 U' R2 U' R2 U R' F' R U R2 U' R' F R
 R' F' R U R2 U' R' F R U' R2 U R2 U R2
 R' U' R U' R U' F U' R' U' R U F' U2 R2 U R
 R' U' R2 U2 F U' R' U R U F' U R' U R' U R