Analysis of xx-top500-191-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ......42.3.8......9...........58.1...4....7.....3......7...4.5....6...3.........8 initial

Autosolve

position: ...1384293284..5179147..386.3.58.142845...7.3...3478.5.738.4.51.8.67..344....3.78 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 7 => CTR => A1: 5,6
* PRF # B9: 5,6 => SOL
* DIS # B9: 9 => CTR => B9: 5,6
* DIS # A1: 6,7 => CTR => A1: 5
* PRF # A1: 5 => SOL
* PRF # C4: 6,7 => SOL
* DIS # C4: 9 => CTR => C4: 6,7
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # C4: 6,7 => SOL
* DIS # C4: 9 => CTR => C4: 6,7
* DIS # A1: 6,7 => CTR => A1: 5
* PRF # A1: 5 => SOL
* PRF # A8: 1,2 => SOL
* DIS # A8: 5 => CTR => A8: 1,2
* DIS # C4: 7 => CTR => C4: 6,9
* DIS # B9: 6,9 => CTR => B9: 5
* PRF # B9: 5 => SOL
* DIS # C8: 1,2 => CTR => C8: 9
* PRF # C8: 9 => SOL
* PRF # C9: 1,2 => SOL
* DIS # C9: 6,9 => CTR => C9: 1,2
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* DIS # C4: 7 => CTR => C4: 6,9
* DIS # E5: 2,9 => CTR => E5: 1,6
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # E5: 6,9 => SOL
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # C9: 2,6 => SOL
* DIS # C9: 1,9 => CTR => C9: 2,6
* DIS # G7: 2,6 => CTR => G7: 9
* PRF # G7: 9 => SOL
* PRF # G7: 2,9 => SOL
* DIS # G7: 6 => CTR => G7: 2,9
* DIS # E5: 2,9 => CTR => E5: 1,6
* DIS # A8: 2 => CTR => A8: 1,5
* PRF # C9: 2,9 => SOL
* DIS # G9: 2,9 => CTR => G9: 6
* PRF # G9: 6 => SOL
* PRF # G7: 2,9 => SOL
* DIS # G7: 6 => CTR => G7: 2,9
* DIS # G9: 2,9 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # C8: 1 => CTR => C8: 2,9
* CNT  46 HDP CHAINS /  54 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # A1: 7 => CTR => A1: 5,6
* PRF A1: 5,6 # B9: 5,6 => SOL
* STA A1: 5,6 + B9: 5,6
* CNT   2 HDP CHAINS /   3 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

......42.3.8......9...........58.1...4....7.....3......7...4.5....6...3.........8 initial
...1384293284..5179147..386.3.58.142845...7.3...3478.5.738.4.51.8.67..344....3.78 autosolve
567138429328496517914752386736589142845261793291347865673824951189675234452913678 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
B1: 5,6
C1: 6,7
E2: 6,9
F2: 6,9
E3: 2,5
F3: 2,5
A4: 6,7
A6: 1,2
B6: 6,9
C6: 1,2
F4: 6,9
D5: 2,9
F5: 1,2
H5: 6,9
H6: 6,9
A7: 2,6
E7: 2,9
F8: 1,5
D9: 2,9
E9: 1,5
G8: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A6,C6: 1.. / A6 = 1  => 21 pairs (_) / C6 = 1  =>  0 pairs (*)
E5,F5: 1.. / E5 = 1  =>  0 pairs (X) / F5 = 1  =>  0 pairs (_)
F8,E9: 1.. / F8 = 1  =>  0 pairs (X) / E9 = 1  =>  0 pairs (_)
C9,E9: 1.. / C9 = 1  =>  0 pairs (X) / E9 = 1  =>  0 pairs (_)
A6,A8: 1.. / A6 = 1  => 21 pairs (_) / A8 = 1  =>  0 pairs (*)
E5,E9: 1.. / E5 = 1  =>  0 pairs (X) / E9 = 1  =>  0 pairs (_)
F5,F8: 1.. / F5 = 1  =>  0 pairs (*) / F8 = 1  =>  0 pairs (X)
E3,F3: 2.. / E3 = 2  =>  0 pairs (X) / F3 = 2  =>  0 pairs (_)
A6,C6: 2.. / A6 = 2  =>  0 pairs (*) / C6 = 2  =>  0 pairs (X)
E7,D9: 2.. / E7 = 2  =>  0 pairs (*) / D9 = 2  =>  0 pairs (X)
D5,D9: 2.. / D5 = 2  =>  0 pairs (*) / D9 = 2  =>  0 pairs (X)
F3,F5: 2.. / F3 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
A1,B1: 5.. / A1 = 5  =>  0 pairs (*) / B1 = 5  =>  0 pairs (X)
E3,F3: 5.. / E3 = 5  =>  0 pairs (*) / F3 = 5  =>  0 pairs (X)
A8,B9: 5.. / A8 = 5  =>  0 pairs (X) / B9 = 5  =>  0 pairs (_)
F8,E9: 5.. / F8 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
A8,F8: 5.. / A8 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
B9,E9: 5.. / B9 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
A1,A8: 5.. / A1 = 5  =>  0 pairs (*) / A8 = 5  =>  0 pairs (X)
B1,B9: 5.. / B1 = 5  =>  0 pairs (X) / B9 = 5  =>  0 pairs (_)
E3,E9: 5.. / E3 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
F3,F8: 5.. / F3 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
E2,F2: 6.. / E2 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
F4,E5: 6.. / F4 = 6  =>  0 pairs (X) / E5 = 6  =>  0 pairs (_)
H5,H6: 6.. / H5 = 6  =>  0 pairs (X) / H6 = 6  =>  0 pairs (_)
G7,G9: 6.. / G7 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
E5,H5: 6.. / E5 = 6  =>  0 pairs (*) / H5 = 6  =>  0 pairs (X)
B6,H6: 6.. / B6 = 6  =>  0 pairs (X) / H6 = 6  =>  0 pairs (_)
A7,G7: 6.. / A7 = 6  =>  0 pairs (*) / G7 = 6  =>  0 pairs (X)
E2,E5: 6.. / E2 = 6  =>  0 pairs (X) / E5 = 6  =>  0 pairs (_)
F2,F4: 6.. / F2 = 6  =>  0 pairs (*) / F4 = 6  =>  0 pairs (X)
A1,C1: 7.. / A1 = 7  =>  0 pairs (X) / C1 = 7  => 21 pairs (_)
A4,C4: 7.. / A4 = 7  => 21 pairs (_) / C4 = 7  =>  0 pairs (X)
A1,A4: 7.. / A1 = 7  =>  0 pairs (X) / A4 = 7  => 21 pairs (_)
C1,C4: 7.. / C1 = 7  => 21 pairs (_) / C4 = 7  =>  0 pairs (X)
E2,F2: 9.. / E2 = 9  =>  0 pairs (*) / F2 = 9  =>  0 pairs (X)
C4,B6: 9.. / C4 = 9  =>  0 pairs (X) / B6 = 9  =>  0 pairs (_)
H5,H6: 9.. / H5 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
E7,D9: 9.. / E7 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
C4,F4: 9.. / C4 = 9  =>  0 pairs (X) / F4 = 9  =>  0 pairs (_)
B6,H6: 9.. / B6 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
E7,G7: 9.. / E7 = 9  =>  0 pairs (X) / G7 = 9  =>  0 pairs (_)
C8,G8: 9.. / C8 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
B6,B9: 9.. / B6 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
D5,D9: 9.. / D5 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
F2,F4: 9.. / F2 = 9  =>  0 pairs (X) / F4 = 9  =>  0 pairs (_)
* DURATION: 0:01:36.280817  START: 09:14:34.334552  END: 09:16:10.615369 2017-05-04
* CP COUNT: (46)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B1,B6,C1,C6,D5,D9,E2,E3,E7,E9,F2,F3,F4,F5,F8,G8,H5,H6)
* ...1384293284..5179147..386.3.58.142845...7.3...3478.5.738.4.51.8.67..344....3.78
* PAIR B1: 5,6 BLK 1
A1: 5,6,7                                # reduction candidate for 5,6
A1: 7 => CTR
* 7561384293284..5179147..386637589142845261793.9.347865273894.51.8.67..344....3.78
A1: 5,6                                  # 21 pairs
* PAIR B1: 5,6 COL B
B9: 5,6,9                                # reduction candidate for 5,6
B9: 5,6 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
B9: 9 => CTR
* .5.1384293284..5179147..386.3.58.142845...7.3.6.347895.738.4.5158.671.34491253678
* PAIR C1: 6,7 BLK 1
A1: 6,7,5                                # reduction candidate for 6,7
A1: 6,7 => CTR
* .5.1384293284..517914725386.3.58.142845.12763162347895.738.4.5158.671.344.1.53.78
A1: 5 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR C1: 6,7 COL C
C4: 6,7,9                                # reduction candidate for 6,7
C4: 6,7 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
C4: 9 => CTR
* ..71384293284..5179147..386739586142845...763.6.347895.738.4.51.8.67.9344962.3.78
* PAIR E2: 6,9 COL E
E5: 6,9,1,2                              # reduction candidate for 6,9
E5: 6,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
E5: 1,2 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895.73894.51.8.67.93449.253678
* PAIR A4: 6,7 BLK 4
C4: 6,7,9                                # reduction candidate for 6,7
C4: 6,7 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
C4: 9 => CTR
* ..71384293284..5179147..386739586142845...763.6.347895.738.4.51.8.67.9344962.3.78
* PAIR A4: 6,7 COL A
A1: 6,7,5                                # reduction candidate for 6,7
A1: 6,7 => CTR
* .5.1384293284..517914725386.3.58.142845.12763162347895.738.4.5158.671.344.1.53.78
A1: 5 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR A6: 1,2 COL A
A8: 1,2,5                                # reduction candidate for 1,2
A8: 1,2 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
A8: 5 => CTR
* .5.138429328469517914725386.3958.142845...7.31.23478.527389465158.6712344.1253978
* PAIR B6: 6,9 BLK 4
C4: 6,9,7                                # reduction candidate for 6,9
C4: 7 => CTR
* ...1384293284..5179147..386.37589142845261793.9.347865.73824951.89675234452913678
C4: 6,9                                  # 21 pairs
* PAIR B6: 6,9 COL B
B9: 6,9,5                                # reduction candidate for 6,9
B9: 6,9 => CTR
* .5.1384293284..517914725386.3.58.142845.12763162347895.738.4.5158.671.344.1.53.78
B9: 5 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR C6: 1,2 COL C
C8: 1,2,9                                # reduction candidate for 1,2
C8: 1,2 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895673894251.8.67.9344912.3678
C8: 9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
C9: 1,2,6,9                              # reduction candidate for 1,2
C9: 1,2 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
C9: 6,9 => CTR
* 5671384293284..517914752386736589142845261793.9.347865673824951.8.675.3445..13.78
* PAIR F4: 6,9 BLK 5
E5: 6,9,1,2                              # reduction candidate for 6,9
E5: 6,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
E5: 1,2 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895.73894.51.8.67.93449.253678
* PAIR F4: 6,9 ROW 4
C4: 6,9,7                                # reduction candidate for 6,9
C4: 7 => CTR
* ...1384293284..5179147..386.37589142845261793.9.347865.73824951.89675234452913678
C4: 6,9                                  # 21 pairs
* PAIR D5: 2,9 BLK 5
E5: 2,9,1,6                              # reduction candidate for 2,9
E5: 2,9 => CTR
* ...1384293284695179147..386.39586142845..1763.6.347895.738.4.51.8.6759344....3.78
E5: 1,6                                  # 22 pairs
* PAIR F5: 1,2 BLK 5
E5: 1,2,6,9                              # reduction candidate for 1,2
E5: 1,2 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895.73894.51.8.67.93449.253678
E5: 6,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR H5: 6,9 ROW 5
E5: 6,9,1,2                              # reduction candidate for 6,9
E5: 6,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
E5: 1,2 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895.73894.51.8.67.93449.253678
* PAIR A7: 2,6 BLK 7
C9: 2,6,1,9                              # reduction candidate for 2,6
C9: 2,6 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
C9: 1,9 => CTR
* ...1384293284..5179147..386.3.589142845261793.9.347865.73824951.89675.344....3.78
* PAIR A7: 2,6 ROW 7
G7: 2,6,9                                # reduction candidate for 2,6
G7: 2,6 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895.73894.51.8.67.93449.253678
G7: 9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR E7: 2,9 ROW 7
G7: 2,9,6                                # reduction candidate for 2,9
G7: 2,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
G7: 6 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895273894651.81675.344..2.3978
* PAIR E7: 2,9 COL E
E5: 2,9,1,6                              # reduction candidate for 2,9
E5: 2,9 => CTR
* ...1384293284695179147..386.39586142845..1763.6.347895.738.4.51.8.6759344....3.78
E5: 1,6                                  # 22 pairs
* PAIR F8: 1,5 ROW 8
A8: 1,5,2                                # reduction candidate for 1,5
A8: 2 => CTR
* 5671384293284..5179147..386736589142845261793192347865673824951.8.67..344....3.78
A8: 1,5                                  # 23 pairs
* PAIR D9: 2,9 ROW 9
C9: 2,9,1,6                              # reduction candidate for 2,9
C9: 2,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
C9: 1,6                                  # 22 pairs
G9: 2,9,6                                # reduction candidate for 2,9
G9: 2,9 => CTR
* ...1384293284695179147..386.395861428459..76316234789527389465158.67.2344..2.3978
G9: 6 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR G8: 2,9 BLK 9
G7: 2,9,6                                # reduction candidate for 2,9
G7: 2,9 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
G7: 6 => CTR
* ...1384293284695179147..386.395861428459..763.6.347895273894651.81675.344..2.3978
G9: 2,9,6                                # reduction candidate for 2,9
G9: 2,9 => CTR
* ...1384293284695179147..386.395861428459..76316234789527389465158.67.2344..2.3978
G9: 6 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* PAIR G8: 2,9 ROW 8
C8: 2,9,1                                # reduction candidate for 2,9
C8: 1 => CTR
* 5671384293284..517914752386736589142845...7.3...3478.5.738.4.51.81675934459213678
C8: 2,9                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-191-base-pr-000.dot
* REASONING
* DIS # A1: 7 => CTR => A1: 5,6
* PRF # B9: 5,6 => SOL
* DIS # B9: 9 => CTR => B9: 5,6
* DIS # A1: 6,7 => CTR => A1: 5
* PRF # A1: 5 => SOL
* PRF # C4: 6,7 => SOL
* DIS # C4: 9 => CTR => C4: 6,7
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # C4: 6,7 => SOL
* DIS # C4: 9 => CTR => C4: 6,7
* DIS # A1: 6,7 => CTR => A1: 5
* PRF # A1: 5 => SOL
* PRF # A8: 1,2 => SOL
* DIS # A8: 5 => CTR => A8: 1,2
* DIS # C4: 7 => CTR => C4: 6,9
* DIS # B9: 6,9 => CTR => B9: 5
* PRF # B9: 5 => SOL
* DIS # C8: 1,2 => CTR => C8: 9
* PRF # C8: 9 => SOL
* PRF # C9: 1,2 => SOL
* DIS # C9: 6,9 => CTR => C9: 1,2
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* DIS # C4: 7 => CTR => C4: 6,9
* DIS # E5: 2,9 => CTR => E5: 1,6
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # E5: 6,9 => SOL
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # C9: 2,6 => SOL
* DIS # C9: 1,9 => CTR => C9: 2,6
* DIS # G7: 2,6 => CTR => G7: 9
* PRF # G7: 9 => SOL
* PRF # G7: 2,9 => SOL
* DIS # G7: 6 => CTR => G7: 2,9
* DIS # E5: 2,9 => CTR => E5: 1,6
* DIS # A8: 2 => CTR => A8: 1,5
* PRF # C9: 2,9 => SOL
* DIS # G9: 2,9 => CTR => G9: 6
* PRF # G9: 6 => SOL
* PRF # G7: 2,9 => SOL
* DIS # G7: 6 => CTR => G7: 2,9
* DIS # G9: 2,9 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # C8: 1 => CTR => C8: 2,9
* CNT  46 HDP CHAINS /  54 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B1,B6,C1,C6,D5,D9,E2,E3,E7,E9,F2,F3,F4,F5,F8,G8,H5,H6)
* ...1384293284..5179147..386.3.58.142845...7.3...3478.5.738.4.51.8.67..344....3.78
* PAIR B1: 5,6 BLK 1
A1: 5,6,7                                # reduction candidate for 5,6
A1: 7 => CTR
* 7561384293284..5179147..386637589142845261793.9.347865273894.51.8.67..344....3.78
* PAIR B1: 5,6 COL B
B9: 5,6,9                                # reduction candidate for 5,6
B9: 5,6 => SOLVED
* 567138429328496517914752386736589142845261793291347865673824951189675234452913678
* DURATION: 0:00:04.654034  START: 09:17:22.099242  END: 09:17:26.753276 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-191-base-pr-001.dot
* REASONING
* DIS # A1: 7 => CTR => A1: 5,6
* PRF A1: 5,6 # B9: 5,6 => SOL
* STA A1: 5,6 + B9: 5,6
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 191

solution: 567138429328496517914752386736589142845261793291347865673824951189675234452913678
info: 1841     FNBTWY   S8.f     1301

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 567138429328496517914752386736589142845261793291347865673824951189675234452913678 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # A1: 5,6 => UNS
* DIS # A1: 7 => CTR => A1: 5,6
* PRF # B9: 5,6 => SOL
* DIS # B9: 9 => CTR => B9: 5,6
* DIS # A1: 6,7 => CTR => A1: 5
* PRF # A1: 5 => SOL
* PRF # C4: 6,7 => SOL
* DIS # C4: 9 => CTR => C4: 6,7
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # C4: 6,7 => SOL
* DIS # C4: 9 => CTR => C4: 6,7
* DIS # A1: 6,7 => CTR => A1: 5
* PRF # A1: 5 => SOL
* PRF # A8: 1,2 => SOL
* DIS # A8: 5 => CTR => A8: 1,2
* INC # C4: 6,9 => UNS
* DIS # C4: 7 => CTR => C4: 6,9
* DIS # B9: 6,9 => CTR => B9: 5
* PRF # B9: 5 => SOL
* DIS # C8: 1,2 => CTR => C8: 9
* PRF # C8: 9 => SOL
* PRF # C9: 1,2 => SOL
* DIS # C9: 6,9 => CTR => C9: 1,2
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* INC # C4: 6,9 => UNS
* DIS # C4: 7 => CTR => C4: 6,9
* DIS # E5: 2,9 => CTR => E5: 1,6
* INC # E5: 1,6 => UNS
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # E5: 6,9 => SOL
* PRF # E5: 6,9 => SOL
* DIS # E5: 1,2 => CTR => E5: 6,9
* PRF # C9: 2,6 => SOL
* DIS # C9: 1,9 => CTR => C9: 2,6
* DIS # G7: 2,6 => CTR => G7: 9
* PRF # G7: 9 => SOL
* PRF # G7: 2,9 => SOL
* DIS # G7: 6 => CTR => G7: 2,9
* DIS # E5: 2,9 => CTR => E5: 1,6
* INC # E5: 1,6 => UNS
* INC # A8: 1,5 => UNS
* DIS # A8: 2 => CTR => A8: 1,5
* PRF # C9: 2,9 => SOL
* INC # C9: 1,6 => UNS
* DIS # G9: 2,9 => CTR => G9: 6
* PRF # G9: 6 => SOL
* PRF # G7: 2,9 => SOL
* DIS # G7: 6 => CTR => G7: 2,9
* DIS # G9: 2,9 => CTR => G9: 6
* PRF # G9: 6 => SOL
* INC # C8: 2,9 => UNS
* DIS # C8: 1 => CTR => C8: 2,9
* CNT  54 HDP CHAINS /  54 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,6 => UNS
* DIS # A1: 7 => CTR => A1: 5,6
* PRF A1: 5,6 # B9: 5,6 => SOL
* STA A1: 5,6 + B9: 5,6
* CNT   3 HDP CHAINS /   3 HYP OPENED