Analysis of zz-www.sudokuoftheday.co.uk-20060604-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006

position: 1..93...8.256........751.2...6..92..8......5..9..2346.........5.8..9....7...8..1. initial

Autosolve

position: 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 4 => CTR => A3: 3,9
* DIS # G2: 3,9 => CTR => G2: 1,7
* DIS # I2: 3,9 => CTR => I2: 1
* DIS # B4: 3,4 => CTR => B4: 7
* DIS # G2: 3,9 => CTR => G2: 1,7
* DIS # I2: 3,9 => CTR => I2: 1
* DIS # A3: 4 => CTR => A3: 3,9
* DIS # G5: 3,9 => CTR => G5: 1
* PRF # G9: 3,9 => SOL
* DIS # G9: 6 => CTR => G9: 3,9
* DIS # B4: 3,4 => CTR => B4: 7
* DIS # B4: 4 => CTR => B4: 3,7
* DIS # E5: 1,7 => CTR => E5: 6
* DIS # E5: 1 => CTR => E5: 6,7
* DIS # F7: 6,7 => CTR => F7: 4
* PRF # F7: 4 => SOL
* DIS # I5: 1,3 => CTR => I5: 9
* DIS # I2: 9 => CTR => I2: 1,3
* PRF # C9: 3,4 => SOL
* DIS # F7: 6,7 => CTR => F7: 4
* PRF # F7: 4 => SOL
* DIS # E5: 1 => CTR => E5: 6,7
* DIS # F7: 7 => CTR => F7: 4,6
* PRF # G9: 3,9 => SOL
* DIS # G9: 6 => CTR => G9: 3,9
* PRF # C7: 3,9 => SOL
* DIS # C7: 4 => CTR => C7: 3,9
* DIS # H2: 7 => CTR => H2: 3,9
* DIS # G8: 3,7 => CTR => G8: 6
* PRF # G8: 6 => SOL
* PRF # H2: 9 => SOL
* CNT  31 HDP CHAINS /  58 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 # A3: 4 => CTR => A3: 3,9
* DIS A3: 3,9 # G2: 3,9 => CTR => G2: 1,7
* DIS A3: 3,9 + G2: 1,7 # I2: 3,9 => CTR => I2: 1
* PRF A3: 3,9 + G2: 1,7 + I2: 1 # G9: 3,9 => SOL
* STA A3: 3,9 + G2: 1,7 + I2: 1 + G9: 3,9
* CNT   4 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

1..93...8.256........751.2...6..92..8......5..9..2346.........5.8..9....7...8..1. initial
167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1. autosolve
167932548325648791948751326476519283832467159591823467619274835283195674754386912 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
A2: 3,9
B3: 3,4
G3: 3,9
A4: 3,4
B5: 3,7
E4: 1,7
F5: 6,7
I4: 1,3
A7: 2,6
A8: 2,6
C8: 3,4
D7: 2,3
E7: 6,7
D9: 2,3
F9: 4,6
H7: 3,9
H8: 3,7
I8: 2,4
I9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,I2: 1.. / G2 = 1  =>  0 pairs (X) / I2 = 1  => 16 pairs (_)
E4,E5: 1.. / E4 = 1  => 19 pairs (_) / E5 = 1  =>  0 pairs (X)
E4,I4: 1.. / E4 = 1  => 19 pairs (_) / I4 = 1  =>  0 pairs (X)
G2,G5: 1.. / G2 = 1  =>  0 pairs (X) / G5 = 1  => 16 pairs (_)
A7,A8: 2.. / A7 = 2  =>  0 pairs (X) / A8 = 2  =>  0 pairs (_)
D7,D9: 2.. / D7 = 2  =>  0 pairs (*) / D9 = 2  =>  0 pairs (X)
I8,I9: 2.. / I8 = 2  =>  0 pairs (X) / I9 = 2  =>  0 pairs (_)
A7,D7: 2.. / A7 = 2  =>  0 pairs (X) / D7 = 2  =>  0 pairs (_)
A8,I8: 2.. / A8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
D9,I9: 2.. / D9 = 2  =>  0 pairs (X) / I9 = 2  =>  0 pairs (_)
D7,D9: 3.. / D7 = 3  =>  0 pairs (X) / D9 = 3  =>  0 pairs (_)
A3,B3: 4.. / A3 = 4  =>  0 pairs (X) / B3 = 4  => 19 pairs (_)
A4,B4: 4.. / A4 = 4  => 19 pairs (_) / B4 = 4  =>  0 pairs (X)
F7,F9: 4.. / F7 = 4  =>  0 pairs (*) / F9 = 4  =>  0 pairs (X)
I8,I9: 4.. / I8 = 4  =>  0 pairs (*) / I9 = 4  =>  0 pairs (X)
C7,F7: 4.. / C7 = 4  =>  0 pairs (X) / F7 = 4  =>  0 pairs (_)
C8,I8: 4.. / C8 = 4  =>  0 pairs (X) / I8 = 4  =>  0 pairs (_)
A3,A4: 4.. / A3 = 4  =>  0 pairs (X) / A4 = 4  => 19 pairs (_)
B3,B4: 4.. / B3 = 4  => 19 pairs (_) / B4 = 4  =>  0 pairs (X)
E5,F5: 6.. / E5 = 6  => 17 pairs (_) / F5 = 6  =>  0 pairs (X)
A7,A8: 6.. / A7 = 6  =>  0 pairs (*) / A8 = 6  =>  0 pairs (X)
G8,G9: 6.. / G8 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
A8,G8: 6.. / A8 = 6  =>  0 pairs (X) / G8 = 6  =>  0 pairs (_)
F9,G9: 6.. / F9 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
E5,E7: 6.. / E5 = 6  => 17 pairs (_) / E7 = 6  =>  0 pairs (X)
G2,H2: 7.. / G2 = 7  => 17 pairs (_) / H2 = 7  =>  0 pairs (X)
B4,B5: 7.. / B4 = 7  => 19 pairs (_) / B5 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  => 17 pairs (_) / F7 = 7  =>  0 pairs (X)
G8,H8: 7.. / G8 = 7  =>  0 pairs (X) / H8 = 7  => 17 pairs (_)
B4,E4: 7.. / B4 = 7  => 19 pairs (_) / E4 = 7  =>  0 pairs (X)
F5,F7: 7.. / F5 = 7  => 17 pairs (_) / F7 = 7  =>  0 pairs (X)
G2,G8: 7.. / G2 = 7  => 17 pairs (_) / G8 = 7  =>  0 pairs (X)
H2,H8: 7.. / H2 = 7  =>  0 pairs (X) / H8 = 7  => 17 pairs (_)
A2,A3: 9.. / A2 = 9  => 22 pairs (_) / A3 = 9  => 21 pairs (_)
G5,I5: 9.. / G5 = 9  =>  0 pairs (X) / I5 = 9  => 21 pairs (_)
C7,C9: 9.. / C7 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
H7,G9: 9.. / H7 = 9  => 21 pairs (_) / G9 = 9  =>  0 pairs (*)
A3,G3: 9.. / A3 = 9  => 21 pairs (_) / G3 = 9  => 22 pairs (_)
C7,H7: 9.. / C7 = 9  =>  0 pairs (*) / H7 = 9  =>  0 pairs (X)
C9,G9: 9.. / C9 = 9  => 21 pairs (_) / G9 = 9  =>  0 pairs (*)
H2,H7: 9.. / H2 = 9  =>  0 pairs (*) / H7 = 9  =>  0 pairs (X)
I2,I5: 9.. / I2 = 9  =>  0 pairs (X) / I5 = 9  => 21 pairs (_)
* DURATION: 0:00:53.751966  START: 23:36:48.855000  END: 23:37:42.606966 2019-04-30
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A7,A8,B3,B5,C8,D7,D9,E4,E7,F5,F9,G3,H7,H8,I4,I8,I9)
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1.
* PAIR A2: 3,9 BLK 1
A3: 3,9,4                                # reduction candidate for 3,9
A3: 4 => CTR
* 167932548925648...438751926346579281872416359591823467.1..6789568.195732759.8..1.
A3: 3,9                                  # 19 pairs
* PAIR A2: 3,9 ROW 2
G2: 3,9,1,7                              # reduction candidate for 3,9
G2: 3,9 => CTR
* 167932548.25648.71..8751.26..65192838324..159591823467.1....895.8.19573.75938.612
G2: 1,7                                  # 20 pairs
H2: 3,9,7                                # reduction candidate for 3,9
H2: 3,9                                  # 17 pairs
I2: 3,9,1                                # reduction candidate for 3,9
I2: 3,9 => CTR
* 167932548.2564817...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612
I2: 1                                    # 16 pairs
* PAIR B3: 3,4 BLK 1
A3: 3,4,9                                # reduction candidate for 3,4
A3: 3,4                                  # 22 pairs
A3: 9                                    # 21 pairs
* PAIR B3: 3,4 COL B
B4: 3,4,7                                # reduction candidate for 3,4
B4: 3,4 => CTR
* 167932548.25648.....8751.26..6579281872416.5.591823467.1..678.568.195..275.284.1.
B4: 7                                    # 19 pairs
* PAIR G3: 3,9 BLK 3
G2: 3,9,1,7                              # reduction candidate for 3,9
G2: 3,9 => CTR
* 167932548.25648.71..8751.26..65192838324..159591823467.1....895.8.19573.75938.612
G2: 1,7                                  # 20 pairs
H2: 3,9,7                                # reduction candidate for 3,9
H2: 3,9                                  # 17 pairs
I2: 3,9,1                                # reduction candidate for 3,9
I2: 3,9 => CTR
* 167932548.2564817...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612
I2: 1                                    # 16 pairs
* PAIR G3: 3,9 ROW 3
A3: 3,9,4                                # reduction candidate for 3,9
A3: 4 => CTR
* 167932548925648...438751926346579281872416359591823467.1..6789568.195732759.8..1.
A3: 3,9                                  # 19 pairs
* PAIR G3: 3,9 COL G
G5: 3,9,1                                # reduction candidate for 3,9
G5: 3,9 => CTR
* 167932548.2564817...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612
G5: 1                                    # 16 pairs
G9: 3,9,6                                # reduction candidate for 3,9
G9: 3,9 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
G9: 6 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....895.8.195...75938.612
* PAIR A4: 3,4 BLK 4
B4: 3,4,7                                # reduction candidate for 3,4
B4: 3,4 => CTR
* 167932548.25648.....8751.26..6579281872416.5.591823467.1..678.568.195..275.284.1.
B4: 7                                    # 19 pairs
* PAIR A4: 3,4 COL A
A3: 3,4,9                                # reduction candidate for 3,4
A3: 3,4                                  # 22 pairs
A3: 9                                    # 21 pairs
* PAIR B5: 3,7 BLK 4
B4: 3,7,4                                # reduction candidate for 3,7
B4: 4 => CTR
* 167932548.25648.....8751.26.46579281872416.5.591823467.1..678.568.195..275.284.1.
B4: 3,7                                  # 19 pairs
* PAIR E4: 1,7 BLK 5
E5: 1,7,6                                # reduction candidate for 1,7
E5: 1,7 => CTR
* 167932548.25648.....8751.26..65.928.8.24.6.5.591823467.1..678.568.195..275.284.1.
E5: 6                                    # 17 pairs
* PAIR F5: 6,7 BLK 5
E5: 6,7,1                                # reduction candidate for 6,7
E5: 1 => CTR
* 167932548.25648.....8751.26..65.928.8.2416.5.591823467.1..678.568.195..275.284.1.
E5: 6,7                                  # 19 pairs
* PAIR F5: 6,7 COL F
F7: 6,7,4                                # reduction candidate for 6,7
F7: 6,7 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.14...895.83195.74759.84.1.
F7: 4 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
* PAIR I4: 1,3 BLK 6
G5: 1,3,9                                # reduction candidate for 1,3
G5: 1,3                                  # 21 pairs
I5: 1,3,9                                # reduction candidate for 1,3
I5: 1,3 => CTR
* 167932548.25648..99487513264.65.928.8.24..95.591823467.1....895.8.195.3.75938.612
I5: 9                                    # 21 pairs
* PAIR I4: 1,3 COL I
I2: 1,3,9                                # reduction candidate for 1,3
I2: 9 => CTR
* 167932548.256481799487513264.65.928.8.24..95.591823467.1....895.8.19573.75938.612
I2: 1,3                                  # 21 pairs
* PAIR C8: 3,4 BLK 7
C7: 3,4,9                                # reduction candidate for 3,4
C7: 3,4                                  # 21 pairs
C9: 3,4,9                                # reduction candidate for 3,4
C9: 3,4 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
C9: 9                                    # 21 pairs
* PAIR E7: 6,7 BLK 8
F7: 6,7,4                                # reduction candidate for 6,7
F7: 6,7 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.14...895.83195.74759.84.1.
F7: 4 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
* PAIR E7: 6,7 COL E
E5: 6,7,1                                # reduction candidate for 6,7
E5: 1 => CTR
* 167932548.25648.....8751.26..65.928.8.2416.5.591823467.1..678.568.195..275.284.1.
E5: 6,7                                  # 19 pairs
* PAIR F9: 4,6 BLK 8
F7: 4,6,7                                # reduction candidate for 4,6
F7: 7 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.14..7895.83195.74759.84.1.
F7: 4,6                                  # 17 pairs
* PAIR H7: 3,9 BLK 9
G9: 3,9,6                                # reduction candidate for 3,9
G9: 3,9 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
G9: 6 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....895.8.195...75938.612
* PAIR H7: 3,9 ROW 7
C7: 3,9,4                                # reduction candidate for 3,9
C7: 3,9 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
C7: 4 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.14...895.83195.74759.84.1.
* PAIR H7: 3,9 COL H
H2: 3,9,7                                # reduction candidate for 3,9
H2: 7 => CTR
* 167932548.25648.7...8751.26..65.928.8.24...5.591823467.1....895.8.19573.75938.612
H2: 3,9                                  # 17 pairs
* PAIR H8: 3,7 BLK 9
G8: 3,7,6                                # reduction candidate for 3,7
G8: 3,7 => CTR
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.568.195..275.28.614
G8: 6 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
* PAIR H8: 3,7 COL H
H2: 3,7,9                                # reduction candidate for 3,7
H2: 9 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
H2: 3,7                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060604-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 4 => CTR => A3: 3,9
* DIS # G2: 3,9 => CTR => G2: 1,7
* DIS # I2: 3,9 => CTR => I2: 1
* DIS # B4: 3,4 => CTR => B4: 7
* DIS # G2: 3,9 => CTR => G2: 1,7
* DIS # I2: 3,9 => CTR => I2: 1
* DIS # A3: 4 => CTR => A3: 3,9
* DIS # G5: 3,9 => CTR => G5: 1
* PRF # G9: 3,9 => SOL
* DIS # G9: 6 => CTR => G9: 3,9
* DIS # B4: 3,4 => CTR => B4: 7
* DIS # B4: 4 => CTR => B4: 3,7
* DIS # E5: 1,7 => CTR => E5: 6
* DIS # E5: 1 => CTR => E5: 6,7
* DIS # F7: 6,7 => CTR => F7: 4
* PRF # F7: 4 => SOL
* DIS # I5: 1,3 => CTR => I5: 9
* DIS # I2: 9 => CTR => I2: 1,3
* PRF # C9: 3,4 => SOL
* DIS # F7: 6,7 => CTR => F7: 4
* PRF # F7: 4 => SOL
* DIS # E5: 1 => CTR => E5: 6,7
* DIS # F7: 7 => CTR => F7: 4,6
* PRF # G9: 3,9 => SOL
* DIS # G9: 6 => CTR => G9: 3,9
* PRF # C7: 3,9 => SOL
* DIS # C7: 4 => CTR => C7: 3,9
* DIS # H2: 7 => CTR => H2: 3,9
* DIS # G8: 3,7 => CTR => G8: 6
* PRF # G8: 6 => SOL
* PRF # H2: 9 => SOL
* CNT  31 HDP CHAINS /  58 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A7,A8,B3,B5,C8,D7,D9,E4,E7,F5,F9,G3,H7,H8,I4,I8,I9)
* 167932548.25648.....8751.26..65.928.8.24...5.591823467.1....8.5.8.195...75..8..1.
* PAIR A2: 3,9 BLK 1
A3: 3,9,4                                # reduction candidate for 3,9
A3: 4 => CTR
* 167932548925648...438751926346579281872416359591823467.1..6789568.195732759.8..1.
* PAIR A2: 3,9 ROW 2
G2: 3,9,1,7                              # reduction candidate for 3,9
G2: 3,9 => CTR
* 167932548.25648.71.48751.264.65192838324..159591823467.1....895.8.19573.75938.612
H2: 3,9,7                                # reduction candidate for 3,9
H2: 3,9                                  # 17 pairs
I2: 3,9,1                                # reduction candidate for 3,9
I2: 3,9 => CTR
* 167932548.2564817..48751.264.65.928.8.24...5.591823467.1....895.8.19573.75938.612
* RESTART
* PAIR RESTART
* PAIR G3: 3,9 COL G
G9: 3,9,6                                # reduction candidate for 3,9
G9: 3,9 => SOLVED
* 167932548325648791948751326476519283832467159591823467619274835283195674754386912
* DURATION: 0:00:05.638925  START: 23:38:24.516019  END: 23:38:30.154944 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060604-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 4 => CTR => A3: 3,9
* DIS A3: 3,9 # G2: 3,9 => CTR => G2: 1,7
* DIS A3: 3,9 + G2: 1,7 # I2: 3,9 => CTR => I2: 1
* PRF A3: 3,9 + G2: 1,7 + I2: 1 # G9: 3,9 => SOL
* STA A3: 3,9 + G2: 1,7 + I2: 1 + G9: 3,9
* CNT   4 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060604, absurd

Solution

position: 167932548325648791948751326476519283832467159591823467619274835283195674754386912 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 # A3: 3,9 => UNS
* DIS # A3: 4 => CTR => A3: 3,9
* DIS # G2: 3,9 => CTR => G2: 1,7
* INC # G2: 1,7 => UNS
* INC # H2: 3,9 => UNS
* DIS # I2: 3,9 => CTR => I2: 1
* INC # I2: 1 => UNS
* INC # A3: 3,4 => UNS
* INC # A3: 9 => UNS
* DIS # B4: 3,4 => CTR => B4: 7
* INC # B4: 7 => UNS
* DIS # G2: 3,9 => CTR => G2: 1,7
* INC # G2: 1,7 => UNS
* INC # H2: 3,9 => UNS
* DIS # I2: 3,9 => CTR => I2: 1
* INC # I2: 1 => UNS
* INC # A3: 3,9 => UNS
* DIS # A3: 4 => CTR => A3: 3,9
* DIS # G5: 3,9 => CTR => G5: 1
* INC # G5: 1 => UNS
* PRF # G9: 3,9 => SOL
* DIS # G9: 6 => CTR => G9: 3,9
* DIS # B4: 3,4 => CTR => B4: 7
* INC # B4: 7 => UNS
* INC # A3: 3,4 => UNS
* INC # A3: 9 => UNS
* INC # B4: 3,7 => UNS
* DIS # B4: 4 => CTR => B4: 3,7
* DIS # E5: 1,7 => CTR => E5: 6
* INC # E5: 6 => UNS
* INC # E5: 6,7 => UNS
* DIS # E5: 1 => CTR => E5: 6,7
* DIS # F7: 6,7 => CTR => F7: 4
* PRF # F7: 4 => SOL
* INC # G5: 1,3 => UNS
* DIS # I5: 1,3 => CTR => I5: 9
* INC # I5: 9 => UNS
* INC # I2: 1,3 => UNS
* DIS # I2: 9 => CTR => I2: 1,3
* INC # C7: 3,4 => UNS
* PRF # C9: 3,4 => SOL
* INC # C9: 9 => UNS
* DIS # F7: 6,7 => CTR => F7: 4
* PRF # F7: 4 => SOL
* INC # E5: 6,7 => UNS
* DIS # E5: 1 => CTR => E5: 6,7
* INC # F7: 4,6 => UNS
* DIS # F7: 7 => CTR => F7: 4,6
* PRF # G9: 3,9 => SOL
* DIS # G9: 6 => CTR => G9: 3,9
* PRF # C7: 3,9 => SOL
* DIS # C7: 4 => CTR => C7: 3,9
* INC # H2: 3,9 => UNS
* DIS # H2: 7 => CTR => H2: 3,9
* DIS # G8: 3,7 => CTR => G8: 6
* PRF # G8: 6 => SOL
* INC # H2: 3,7 => UNS
* PRF # H2: 9 => SOL
* CNT  58 HDP CHAINS /  58 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 3,9 => UNS
* DIS # A3: 4 => CTR => A3: 3,9
* DIS A3: 3,9 # G2: 3,9 => CTR => G2: 1,7
* INC A3: 3,9 + G2: 1,7 # H2: 3,9 => UNS
* DIS A3: 3,9 + G2: 1,7 # I2: 3,9 => CTR => I2: 1
* PRF A3: 3,9 + G2: 1,7 + I2: 1 # G9: 3,9 => SOL
* STA A3: 3,9 + G2: 1,7 + I2: 1 + G9: 3,9
* CNT   6 HDP CHAINS /   6 HYP OPENED