SD corner 3-cycle method -- a variation of TuRBo

[leeo]

I was half-way into learning all of the 18 algs for TuRBo corners, when in rebellion, I stared searching for other commutators -- I found it difficult to warp my mind's eye to clockwise U-Face corner cycles after learning nine of the counter-clockwise U-Face corner cycles. A computer search reveled that learning the "opposite-direction" cycles only helps reduce the setup length in under 30% of all cases. After picking some random cycles to include and completing a computer search catalog, I stumbled into this method, which only requires *6* corner-cycle algs. This can be an entry-way into the BH method. I call this the Solid-Diagonal (SD) method.

The basic idea is that the target from the buffer is the solid-diagonal opposite cubie from the buffer. For example, a ULB buffer targets the FRD or RDF cubie. For a three-cycle method, the secondary, or helper, is on the same face as the target and diagonally opposite: in my case one of BLD, DBL or LDB. A computer search from these six algs shows the following properites: In all cases, only three or fewer setups are required. Additionally, all 378 of the setups can completed without disturbing the buffer. All of the algorighms have been verified not to twist the center face, and thus are "super-cube" safe.

In the chart below "(11f 3ff)" refers to the number of face turns "(11f)", and face double turns "(3ff)". The comment after "//" gives a short name for the algorithm based on Steven Arducci's facelet letter scheme in his video _How to Memorize for Blind Solving_. The short names for the algorithms are based on what a blind solver would read after the algorithm is turned onto a solved cube.

ULB -> DFR -> DBL : L B2 R' B' L2 B R B' L2 B' L' (11f 3ff) // _VY

ULB -> DFR -> LDB : x Uw' L' U2 L Uw B' U2 B x' (8f 2ff) // _RY

ULB -> DFR -> BLD : x' U R' U' L' U R U' L x (8f 0ff) // _OY


ULB -> RDF -> DBL : D L2 U R' U' L2 U R D' U' (10f 2ff) // _VJ

ULB -> RDF -> LDB : D2 L U L' D2 L U' L' (8f 2ff) // _RJ

ULB -> RDF -> BLD : L B' R2 B L' B' R2 B (8f 2ff) // _OJ


With the secondary facelet (DBL, LDB or BLD) diagonally opposite and on the same face as the target from the buffer (DFR or RDF), it is not necessary to learn the opposite or inverse algorithms. in two cases, a D2 setup move is enough to give the inverse. Note, in the second case listed it can be recognized that the D2 setup cancels the first D2 in the alg.


ULB -> DBL -> DFR == D2 {ULB -> DFR -> DBL} D2 // _YV == D2 {_VY} D2

ULB -> LDB -> RDF == D2 {ULB -> RDF -> LDB} D2 // _JR == D2 {_RJ} D2

in two cases, a D2 setup to another alg in the list generates an inverse.


ULB -> DBL -> RDF == D2 {ULB -> DFR -> LDB} D2 // _JV == D2 {_RY} D2

ULB -> LDB -> DFR == D2 {ULB -> DFR -> BLD} D2 // _YR == D2 {_OY} D2


Unlike in TuRBo, it is not necessary in SD to learn ULB -> FRD -> DBL, or other FRD target algorithms, because with the target from the buffer being as far removed from the buffer as possible, that facelet of the target cubie can be rotated into place with setup moves.


ULB -> FRD -> DBL == R F {ULB -> RDF -> DBL} F' R'
// _VG == R F {_VJ} F' R'

ULB -> FRD -> LDB == R F {ULB -> RDF -> LDB} F' R'
// _RG == R F {_RJ} F' R'

ULB -> FRD -> BLD == R F {ULB -> RDF -> BLD} F' R'
// _OG == R F {_OJ} F' R'


With this, as a D2 applied to two of the 6 algorighms gives a FRD target, but this can be modified with the target cubie rotation to give the inverse.


ULB -> DFR -> BLD == D2 R F {ULB -> RDF -> DBL} F' R' D2
// _YO == D2 R F {_VJ} F' R' D2

ULB -> RDF -> BLD == D2 R F {ULB -> RDF -> LDB} F' R' D2
// _JO == D2 R F {_RJ} F' R' D2


Knowing some of the TuRBo algs can be an aid by giving shorter sequences, saving up to six moves. However, this is not strictly required in SD. In fact, it can be illustrative to show how setup moves can give the same results as some of the TuRBo algorighms:

ULB -> UBR -> URF: "_ACD" with setup moves F2 R D
  gives 
  ULB -> DFR -> LDB (_RY) then undo setup: D' R' F2


ULB -> URF -> UBR: "_ADC" with setup moves R' D2 R'
 gives
  ULB -> DFR -> BLD (_OY) then undo setup: R D2 R



ULB -> BRU -> RFU: "_AIM" with setup moves R D R2
  gives
  ULB -> RDF -> DBL (_JV) then undo setup: R2 D' R'


ULB -> RFU -> BRU: "_AMI" with setup moves R' D2 F
  gives
  ULB -> RDF -> LDB (_RJ) then undo setup: F' D2 R



ULB -> RUB -> FUR: "_AHL" with setup moves R D R2
  gives
  ULB -> DFR -> BLD (_OY) then undo setup: R2 D' R'


ULB -> FUR -> RUB: "_ALH" with setup moves F2 D' R2
  gives
  ULB -> RDF -> LDB (_RJ) then undo setup: R2 D F2




ULB -> UBR -> FUR: "_AHD" with setup moves R D R2
  gives
  ULB -> RDF -> BLD (_OJ) then undo setup: R2 D' R'


ULB -> FUR -> UBR: "_ADH" with setup moves R' D2 R'
  gives
  ULB -> DFR -> DBL (_VY) then undo setup R D2 R



ULB -> BRU -> URF: "_ACM" with setup moves F2 R D
  gives
  ULB -> DFR -> DBL (_VY) then undo setup D' R' F2


ULB -> URF -> BRU: "_AMC" with setup moves R' D2 F
  gives
  ULB -> RDF -> BLD (_OJ) then undo setup: F' D2 R



ULB -> RUB -> RFU: "_AIL" with setup moves R D R2
  gives
  ULB -> RDF -> BLD (_OJ) then undo setup: R2 D' R'


ULB -> RFU -> RUB: "_ALI" with setup moves R' D2 R'
  gives
  ULB -> RDF -> LDB (_RJ) then undo setup: R D2 R




ULB -> UBR -> RFU: "_AID" with setup moves R D R2
  gives
  ULB -> RDF -> LDB (_RJ) then undo setup: R2 D' R'


ULB -> RFU -> UBR: "_ADI" with setup moves R' D2 R'
  gives
  ULB -> DFR -> LDB (_RY) then undo setup: R D2 R



ULB -> BRU -> FUR: "_AHM" with setup moves R' D R2
  gives
  ULB -> DFR -> DBL (_VY) then undo setup: R D2 R


ULB -> FUR -> BRU: "_AMH" with setup moves R2 D R
  gives
  ULB -> RDF -> LDB (_RJ) then undo setup: R' D' R2



ULB -> RUB -> URF: "_ACL" with setup moves F2 R D
  gives
  ULB -> DFR -> BLD (_OY) then undo setup: D' R' F2


ULB -> URF -> RUB: "_ALC" with setup moves R' D2 R'
  gives
  ULB -> RDF -> BLD (_OJ) then undo setup: R D2 R

-- Example corner solve --


Scramble: B F' D U2 F2 U' R' F U2 F2 L' U2 B' D' U2 F2 D' U2 L' B F' L2 D2 B2 L'

A BLD solver reading the corners with a lettering system will observe "_ADG_BURHK" or something similar depending on the letter assignments. In this system the ULB buffer is _A, and _ADG gives us the three-cycle ULB -> FRD -> UBR which with the setup moves D2 R2 gives us the cycle ULB -> DFR -> BLD (_OY). Executing this and then undoing the setup with R2 D2 will solve DFR and BLD.

A BLD solver if permitted, would then read "_BURHK", since the buffer is also solved at this point. Now we can break into the remaining cycle by executing "_ABURHKB" as three additional 3-cycles: "_ABU", "_ARH", "_AKB" which will then complete the solution of the corners.

"_ABU": ULB -> DLF -> UFL with setup moves D' F2
gives ULB -> DFR -> DBL (_VY). Then undo the setup: F2 D

"_ARH": ULB -> FUR -> LDB with setup moves F D2
gives ULB -> RDF -> BLD (_OJ). Then undo the setup: D2 F

"_AKB": ULB -> RBD -> UFL with setup moves F2 D2 F'
gives ULB -> DFR -> DBL (_VY). Then undo the setup: F D2 F2

-- -- --

To summarize, The goal of each setup is to always place the target from the buffer ULB to the solid-diagonally opposite cubie on the facelet DFR or RDF. At the same time, the next reading is placed on any facelet of the cubie in the same face diagonally across the target: DBL, BLD, or LDB. With a lettering scheme for each of the corner facelets, it may help to visualize the progression of the letter pair to solve into the target sequence with the setup moves. For instance, the final 3-cycle "_AKB" changes with the F2 move to "_AKY" which changes with the D2 move to "_ASV" which changes with the F' move to "_AYV". This is solvable with the (_VY) target sequence. Then as the setups are undone, the progression works back to "_AKB" similarly: F changes "_AYV" to "_ASV"; D2 changes "_ASV" to "_AKY"; and finally F2 changes "_AKY" back to"_AKB".

-- S. Lee Odegard, January 2015

 

[Stefan]

Can you do your computer search for ULB -> (URF/RFU/FUR) -> (DRB/RBD/BDR) as well? That covers more cases (nine vs your six) and if you allow rotations around the UBR-DLF axis, you only need five algs (e.g., x U' L U R2 U' r' F R2 and z U' L U R2 U' r' F R2+rotateback and (y x2) U' L U R2 U' r' F R2+rotateback share the same alg).

 

[leeo]

Can you do your computer search for ULB -> (URF/RFU/FUR) -> (DRB/RBD/BDR) as well? That covers more cases (nine vs your six) and if you allow rotations around the UBR-DLF axis, you only need five algs (e.g., x U' L U R2 U' r' F R2 and z U' L U R2 U' r' F R2+rotateback and (y x2) U' L U R2 U' r' F R2+rotateback share the same alg).

This alg. set can be turned into the SD alg. set with a F or R setup move. On the same vein, I do accomplish the a pair of in-place edge twists with a similar strategy. To twist LBU -> ULB along with the opposite twist RDF -> DFR:


R' Fw2 L D' F2 D L' Fw2 R U' F2 U (12f 4ff)

the inverse can be accomplished with the whole-cube rotation setup to exchange ULB with DFR:

x2 y' R' Fw2 L D' F2 D L' Fw2 R U' F2 U y x2

" x2 y' " describes the rotation along the LF - BR axis of two-fold symmetry. I execute this by whole-cube rotating the FL edge turning it into an LF edge. This was simply a means for myself not to have to learn the opposite alg.

-----

If I instead allow whole-cube rotations along the axis of three-fold symmetry of the solid diagonal from the buffer to the target of SD, I find this can simplify some of the setups I traditionally have been using.

for instanace, given
ULB -> DFR -> DBL : L B2 R' B' L2 B R B' L2 B' L' (11f 3ff) // _VY

ULB -> RFD -> LUF : x' y {_VY} y' x // _TJ
my traditional setup: D2 F2 {_RJ} F2 D2 // _TJ 2 _TR 2 _JR

ULB -> FRD -> BRU -> x z {_VY} z' x' // _MG
my traditional setup: D2 R' F {_OJ} F' R D2 // _MG 2 _MO _CO _JO

This looks promising.... I have been searching for an alg. set that only requires a maximum of two setups to reach all 378 cases from a fixed buffer.

 

[qqwref]

This is a very neat idea. I really like how you actually did a computer search to verify that your set of algs had the qualities you want.

(This may just me knowing nothing about BLD and being lazy, but... some images of the cycles would be nice Especially when you start saying stuff like _ABU - is that Speffz?)

 

[leeo]

This is a very neat idea. I really like how you actually did a computer search to verify that your set of algs had the qualities you want.

(This may just me knowing nothing about BLD and being lazy, but... some images of the cycles would be nice Especially when you start saying stuff like _ABU - is that Speffz?)

 

[lerenard]

View attachment 4932

That's a weird lettering scheme. I thought everything was supposed to go clockwise?
I've never had a BLD success, so can't really critique your idea, but it does look cool.

 

[supercavitation]

That's a weird lettering scheme. I thought everything was supposed to go clockwise?
I've never had a BLD success, so can't really critique your idea, but it does look cool.

That's standard speffz adapted for a big cube (in this case, a 7x7).

EDIT: I'm wrong, scroll down.

 

[Stefan]

That's standard speffz adapted for a big cube (in this case, a 7x7).

So the wiki, which includes the picture for the 7x7 that was probably used for the above altered image, has been wrong for over four years and nobody noticed?

 

[supercavitation]

So the wiki, which includes the picture for the 7x7 that was probably used for the above altered image, has been wrong for over four years and nobody noticed?

...I thought that was the picture from the wiki. I did not notice that it was altered by a y'.

 

[leeo]

Stefan is correct -- The system I learned was not Speffz, and the best diagram I could find was indeed the picture from the wiki. I am guilty of not properly crediting the source and mentioning that I altered it to match Steven Arducci's letter assignments. To convert these letter assignments into Speffz letter assignments, you may use this permutation presented in cycle notation:

(A)(BD)(C)(EIMQ)(FLNT)(GKOS)(HJPR)(U)(VX)(W)

The immediate next letter in the cycle converts from Steven Arducci's system to Speffz, and the immediate previous in the cycle converts from Speffz to Steven Arducci's, with the exception of "X". One convention Steven Arducci suggested that I adopted is to employ _Y instead of "X", since it is easier to come up with names, nouns, adjectives, verbs or adverbs beginning with or otherwise involving "Y" than with "X". So, if the conversion arrives at "X" and if converting to Steven Arducci's system substitute _Y. Converting the other way requires that _Y first be exchanged for "X".

If the character you arrive at is a parenthesis, skip to the matching parenthesis and continue in the same direction.

-----

I find that having a lettering assignment system is crucial to efficiently navigating through the setup moves.

Following Stephan's advice, I indeed found an algorithm set that requires only *2* setup moves to reach all 378 cases from a fixed buffer. This requires one more algorithm from the six I introduced earlier, and two additional move types.

ULB -> FRD -> URF : F D F' U2 F D' F' U2 (8f 2ff) // _CG

Its inverse can be generated with the simple U2 setup; or, if you prefer, to simply move the final U2 in the alg. to the beginning.

I now present my canonical compact setup table. Since the letter assignments "use up" all the letters, to keep the table readable, different move types are indicated instead with numbers:

2 -- a double or 180-degree face turn, such as U2 F2, etc.
3 -- a two-layer move, or "w" move using WCF notation ( "3" and "W" look somewhat similar).
4 -- a whole cube rotation, such as x, y', z and so forth.
5 -- a slice move, M, E' or S or such ("5" and "S" also look somewhat similar).
6 -- (new) a whole-cube rotation along the axis of three-fold symmetry from the buffer to the target of SD: thus either x' y or x z
7 -- (new) actually 3 face-turn metric moves: move the buffer cubie "out of the way" with a U or U' move, then move either "L" or "B", then restore the buffer with the opposite U move.

Technically, then in the face turn metric, code 6 is not a move and code 7 is actually three moves. Thus it would be more accurate to say that I have found an algorithm set that only requires two setup points of memory. After the setup and one of the 7 algorithms, the setup must, of course, be "undone" in reverse order.

Here is the compact canonical table describing the setups needed to reach all 378 corner 3-cycles with an _A buffer

_BC  72  UV JV -- _BD  7 BR 2YR 
_BF BR 2YR -- _BG 2BO 2YO -- _BH  72 BR 2YR
_BI  72  UO JO -- _BJ 2BR 2YR -- _BK BO 2YO -- _BL 6  LO 2JO
_BM 6  LV 2JV -- _BN BR 2YR -- _BO 2YO
_BR 2YR -- _BS BO 2YO
_BU BV 2YV -- _BV 2YV -- _BW BV 2YV -- _BY 2BV 2YV

_CB 6  UO JO -- _CD JD  7 JR %
_CE 6  UR JR -- _CF CR JR -- _CG 2CO JO
_CJ 2CR JR -- _CK CO JO -- _CL JL  7 JO % -- _CM  GC %
_CN CR JR -- _CO JO
_CR JR -- _CS CO JO -- _CT 6  UV JV
_CU CV JV -- _CV JV -- _CW CV JV -- _CY 2CV JV

_DB  7 DO 2YO -- _DC  72 DV 2YV
_DE  7 DR 2YR -- _DF DR 2YR -- _DG 2DO 2YO -- _DH  72 DR 2YR
_DI  72 DO 2YO -- _DJ 2DR 2YR -- _DK DO 2YO
_DN DR 2YR -- _DO 2YO
_DR 2YR -- _DS DO 2YO -- _DT  7 DV 2YV
_DU DV 2YV -- _DV 2YV -- _DW DV 2YV -- _DY 2DV 2YV

_EC  72  SV YV -- _ED 6  DR 2YR
_EF  7  HV YV -- _EG  7 RG 2 JO % -- _EH  72  SR YR
_EI  72  SO YO -- _EJ  7 RJ 2 JR % -- _EK FK  JO %
_EL 6  DO 2YO -- _EM 6  DV 2YV -- _EN FN  JR % -- _EO HO YO
_ER HR YR -- _ES  7  HR YR -- _EU  7  HO YO
_EV HV YV -- _EW FW  JV % -- _EY 2 GB 6  JO %

_FB 6  NO YO -- _FC  7 FK  JO % -- _FD 6  HR YR
_FE 6  NR YR -- _FG 2 NO YO -- _FH 2FN  JR %
_FI 2FK  JO % -- _FJ 2 NR YR -- _FK  JO % -- _FL FK  JO %
_FM FW  JV % -- _FN  JR % -- _FO 2HO YO
_FR 2HR YR -- _FT 6  NV YV
_FV 2HV YV -- _FW  JV % -- _FY FN  JR %

_GB 6  JO % -- _GC % -- _GD 6  YR %
_GE 6  JR % -- _GF  SR YR -- _GH 6  YN  7 YO %
_GI  7 GB 6  JO % -- _GK  KO JO -- _GL 6  YO %
_GM 6  YV % -- _GN  KR JR -- _GO CO JO
_GR HR YR -- _GS  SO YO -- _GT 6  JV %
_GU  SV YV -- _GV CV JV -- _GW  KV JV

_HB YB  7 YO % -- _HD 6  NR YR
_HE YE  7 YR % -- _HF HR YR -- _HG 2HO YO
_HJ 2HR YR -- _HK HO YO -- _HL 6  NO YO
_HM 6  NV YV -- _HN HR YR -- _HO YO
_HR YR -- _HS HO YO -- _HT  GC %
_HU HV YV -- _HV YV -- _HW HV YV -- _HY 2HV YV

_IB 6  SO YO -- _ID 6  KR JR
_IE 6  SR YR -- _IF IR YR -- _IG 2IO JO
_IJ 2IR YR -- _IK IO JO -- _IL 6  KO JO
_IM 6  KV JV -- _IN IR YR -- _IO JO
_IR YR -- _IS IO JO -- _IT 6  SV YV
_IU IV JV -- _IV JV -- _IW IV JV -- _IY 2IV JV

_JB  7 JO % -- _JC  72 JV % -- _JD  7 JR %
_JE 6  YR % -- _JF  7 JV % -- _JH  72 JR %
_JI  72 JO % -- _JK  NO YO -- _JL  7 JO %
_JM  7 JV % -- _JN  NR YR -- _JO %
_JR % -- _JS  7 JR % -- _JT  7 JV %
_JU  7 JO % -- _JV % -- _JW  7 JR %

_KB 6  IO JO -- _KC GC -- _KD 6  SR YR
_KE 6  IR YR -- _KF  7 KV JV -- _KG 2 SO YO -- _KH  72 KR JR
_KI  72 KO JO -- _KJ 2 SR YR -- _KL 6  SO YO
_KM 6  SV YV -- _KO JO
_KR JR -- _KS  7 KR JR -- _KT 6  IV JV
_KU  7 KO JO -- _KV JV -- _KY 2 SV YV

_LB  7 LO 2JO -- _LC  72 LV 2JV
_LE 6  BR 2YR -- _LF LR 2JR -- _LG 2LO 2JO -- _LH  72  NR YR
_LI  72 LO 2JO -- _LJ 2LR 2JR -- _LK LO 2JO
_LN LR 2JR -- _LO 2JO 
_LR 2JR -- _LS LO 2JO -- _LT  7 LV 2JV
_LU LV 2JV -- _LV 2JV -- _LW LV 2JV -- _LY 2LV 2JV

_MB 6  TO 2JO -- _MC  72  KV JV
_ME 6  TR 2JR -- _MF WF  YR % -- _MG  7 VG 2 YO % -- _MH  72  KR JR
_MI  72  KO JO -- _MJ 2 GL 6  YO % -- _MK  7  CV JV
_MN  7  CO JO -- _MO CO JO
_MR CR JR -- _MS WS  YO % -- _MT 6  TV 2JV
_MU WU  YV % -- _MV CV JV -- _MW  7  CR JR -- _MY 2 GD 6  YR %

_NB NS  JO % -- _NC 2NU  JV % -- _ND  7  IR YR
_NE 6  HR YR -- _NF  JR % -- _NG NF  JR % -- _NH  72 NR YR
_NI 2NS  JO % -- _NJ NU  JV % -- _NL  7  IO JO
_NM  7  IV JV -- _NO YO
_NR YR -- _NS  JO % -- _NT NU  JV %
_NU  JV % -- _NV YV -- _NY NS  JO %

_OB 6  LO 2JO -- _OC 2GC -- _OD 6  BR 2YR
_OE 6  LR 2JR -- _OF  KR JR -- _OG OC 2GC -- _OH  72  IR YR
_OI  72  IO JO -- _OJ OC 2GC -- _OK  SO YO -- _OL 6  BO 2YO
_OM 6  BV 2YV -- _ON  SR YR
_OS  KO JO -- _OT 6  LV 2JV
_OU  KV JV -- _OW  SV YV -- _OY 2 GV  72 GC %

_RB 6  DO 2YO -- _RC RG 2 JO % -- _RD 2RY 2 JV %
_RE 6  DR 2YR -- _RF  NR YR -- _RG 2 JO % -- _RH RG 2 JO %
_RI  72  HO YO -- _RJ 2 JR % -- _RK RJ 2 JR % -- _RL 2JL  7 JO %
_RM 2RG 2 JO % -- _RN  7  DO 2YO
_RS  NO YO -- _RT 2RJ 2 JR %
_RU  NV YV -- _RW RG 2 JO % -- _RY 2 JV %

_SB 6  KO JO -- _SC GC -- _SD 6  IR YR
_SE 6  KR JR -- _SG 2 KO JO -- _SH  72 SR YR
_SI  72 SO YO -- _SJ 2 KR JR -- _SK  7 SV YV -- _SL 6  IO JO
_SM 6  IV JV -- _SN  7 SO YO -- _SO YO
_SR YR -- _ST 6  KV JV -- 
_SV YV -- _SW  7 SR YR -- _SY 2 KV JV

_TC 2 JU  7 JO % -- _TD  7 TR 2JR
_TF TR 2JR -- _TG 2TO 2JO -- _TH  72 TR 2JR
_TI  72 TO 2JO -- _TJ 2TR 2JR -- _TK TO 2JO -- _TL  7 TO 2JO
_TM  7 TV 2JV -- _TN TR 2JR -- _TO 2JO
_TR 2JR -- _TS TO 2JO
_TU TV 2JV -- _TV 2JV -- _TW TV 2JV -- _TY 2TV 2JV

_UB  7  IO JO -- _UC  72 UV JV -- _UD UN  YR %
_UE  7  IR YR -- _UG UW  YV % -- _UH 2UN  YR %
_UI  72 UO JO -- _UJ UK  YO % -- _UK  YO % -- _UL 6  CO JO
_UM 6  CV JV -- _UN  YR % -- _UO JO
_UR JR -- _UT  JU  7 JO % 
_UV JV -- _UW  YV % -- _UY UN  YR %

_VB 2YB  7 YO % -- _VC VG 2 YO % -- _VD 6  TR 2JR
_VE 2VG 2 YO % -- _VF VG 2 YO % -- _VG 2 YO % -- _VH VG 2 YO %
_VI VJ 2 YR % -- _VJ 2 YR % -- _VK  UO JO -- _VL 6  TO 2JO
_VM 2VG 2 YO % -- _VN  UR JR
_VS  7  TR 2JR -- _VT 2VJ 2 YR %
_VU VJ 2 YR % -- _VW  UV JV -- _VY 2 YV %

_WB 6  CO JO -- _WC 2WU  YV % -- _WD 6  UR JR
_WE WF  YR % -- _WF  YR % -- _WG 2 UO JO -- _WH 2WF  YR %
_WI 2WS  YO % -- _WJ 2 UR JR -- _WL 6  UO JO
_WM 6  UV JV -- _WO 2CO JO -- _WR 2CR JR
_WS  YO % -- _WT 6  CV JV
_WU  YV % -- _WV 2CV JV -- _WY WS  YO %

_YB  7 YO % -- _YC  72 YV % -- _YD  7 YR %
_YE  7 YR % -- _YF  UR JR -- _YH  72 YR %
_YI  72 YO % -- _YK  7 YV % -- _YL 6  JO %
_YM 6  JV % -- _YN  7 YO % -- _YO %
_YR % -- _YS  UO JO -- _YT  7 YV %
_YU  7 YO % -- _YV % -- _YW  7 YR %

Explanation: The "%" either indicates that no setup moves are required, or flags that the setup moves adjust both facelets at the same time or in an order reversed from that which I prefer. Since the computer search strictly prefers setups with shorter length, this causes setups in a preferred order to be selected if such exists.

The table is deliberately vague to act as an exercise in following the setup moves into the target sequence. For instance, "_BJ 2BR 2YR" describes the solution for the letter pair "BJ" as read by a BLD solver. "_BJ 2BR" indicates that a 180-degree turn exchanges the corner cubies at _B and _J to arrive at the same corner cubies at _B and _R. So it is only _J to _R that changes. With a thorough knowledge of the letter system, it can be easily seen that a D2 move is indicated. The second, "BR 2YR" indicates that a 180-degree turn exchanges the corner cubies at _B and _R to arrive at the same corner cubies at _Y and _R. So it is only _B to _Y that changes... an F2 move. arriving at "YR" is solvable with the "_RY" algorithm. Now to undo the setup, simply read the table backwards, "_YR 2BR 2BJ" with the same method.

If there is interest, it should be a simple matter to translate the table into Speffz or any other letter scheme by applying the permutation. --LeeO