Orientation-Preserving F2L

Last F2L pair cases with all U-pieces correctly oriented have easy recognition. These algorithms solve the last pair and the last-layer orientation, leaving PLL. Of course, the list excludes pair patterns where the corner or the edge is incorrectly oriented in place. The better algorithms may be worth learning.

Although certain algorithms had been known, this page (first published in August 2010) is the first complete list of such cases.

Io
(U)L'U2RUR'U2'L
winter variation case
(U')L'U2RU'R'U2'L
inverse; actually better
B'URU'R'U'B
for reference; inverse also works
If
yU'RU2'L'U'LU2'R'
winter varitaion case
yURU2'L'ULU2'R'
inverse; actually better
y'R'F'RUR'U'R'FR2
from Mario Laurent
y'FU'R'URUF'
for reference; inverse also works
To
RURDR'U2RD'R'U2'R'
cancellation with headlights OLL; inverse of R1
(U)R'UR'UR'U'R2UR'U2R
inverse of L1
Tf
y'R'U'R'D'RU2'R'DRU2R
cancellation with headlights OLL; inverse of R2
y'U'RU'RU'RUR2U'RU2'R'
inverse of L2
Qo
(U')L'U2'LURU2'L'U'LR'
y2(U')R'U2RULU2R'U'RL'
same algorithm
Qf
y'ULU2'L'U'R'U2LUL'R
yURU2'R'U'L'U2RUR'L
same algorithm
So
LRU2'L'U2'R'U2'LU2'L'
L2F2L'F2L'U2LU2L'
Sf
yR2F2'RF2'-RU2'R'U2'R
y'L'R'U2'LU2'RU2'L'U2'L
yR'L'U2RU2LU2R'U2R
same algorithm
Jo
RULU2'R'U2RU2'L'U2R'
RU2LU2R'U2RU2L'U'R'
inverse
U'LU'RUL'RUR2UR2U2R2
Jf
y'UL'UR'U'LR'U'R2U'R2U2'R2
y'U'R2U2'R2'UR2URL'URU'L
inverse
y'R'U'L'U2RU2R'U2LU2R
Lo
R'U2'RU'R2'URU'RU'R
inverse of T1, second algorithm
Lf
y'RU2'R'UR2U'R'UR'UR'
inverse of T2, second algorithm
Ro
(U')RU'R'U2'RULU'R'UL'
reduction to CLS
(U')RU2'RDR'U2RD'R'U'R'
inverse of T1, first algorithm
Rf
(Dw)R'URU2'R'U'L'URU'L
reduction to CLS
(Dw)R'U2R'D'RU2'R'DRUR
inverse of T2, first algorithm
Ko
RU'F'RwUR'U'Rw'F
RU'F'LFR'F'L'F without double layer
(U2)F'RwURU'Rw'FUR'
inverse
(U)LD'L'U'LDL'RU'R'
easier after x2?
Kf
y'R'UBRw'U'RULU'x
No
RU2'R'U'RU2'R'URU2'R'
from Lucas Garron; self inverse
RU2'R'U'L'RUR'U'L
F2'L'ULU2L'U'LF2'
self inverse
Nf
y'R'U2'RULR'U'RUL'
yF2RU'R'U2'RUR'F2
no regrip; self inverse
Uo
RUR'URU2'RUR'URU2'R2
U'RUR2U2R2UR2UR2UR'
Uf
y'R'U'RU'R'U2'R'U'RU'R'U2'R2
y'UR'U'R2U2R2U'R2U'R2U'R
Vo
RU'R'U2'RUR'
self inverse
Vf
(y')R'URU2'R'U'R
self inverse
Mo
R2UR'URU2'R'U'R'
(U)RURU2R'U'RU'R2
inverse; (U)RUR' - usual F2L R2U2... with cancellation
Mf
y'R2U'RU'R'U2'RUR
y'U'R'U'R'U2RUR'UR2
inverse
Ao
R'U'R'U'R'URUR
(U)R'U'R'U'R2URUR
(U2)R'U'R'U'RURUR
(U')F'RUR'U'RwURw'U'F'
conjugated ELL; also inverse
Af
y'RURURU'R'U'R'
(U')y'RURUR2U'R'U'R'
(U2)y'RURUR'U'R'U'R'
(U)yFRUR'U'RwURw'U'F'
conjugated ELL; faster from this direction; also inverse
G1
U'R'D'RUR'DR
CLS case;commutator
UR'D'RU'R'DR
commutator
LD'L'ULDL'
commutator
G2
yR'DRU'R'D'R
commutator
C1
yU'R'URU'R'UL'U'RUR'U'RUL
commutator to rotate two corners
C2
L'RUR'U'LRU2R'U'RUR'
CLS case; from Lucas Garron and Jeremy Fleischman
yU'RUR'U'RUL'U'R'URU'R'UL
commutator to rotate two corners
X
(U')RU'R'URU2'R'U'RUR'
CLS case; reduction by RU'R'; from Lucas Garron
y'UR'URU'R'U2'RUR'U'R
same algorithm; possible for FL/BL slots
(U)RU2'R'U2R'F2RU2'RU2'R'F2
from Lucas Garron; for Per Special; variations [F2; [R: U*; U*]]
R'FRF'R'FRF'R'FRF'
double transposition
y'RB'R'BRB'R'BRB'R'B
same algorithm; possible for FL/BL slots