Analysis of xx-top500-080-base.sdk
Contents
Original Sudoku
level: medium
position: 82..3.......5...4..........3.....8.2...4.7......1......64....7.....1.3....5...... initial
Autosolve
position: 82..347.....5...4.45..71...347...812...4.7.3....1.34.7.643...7.....1.3.4.35.4.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 6,9 => CTR => C1: 1 * DIS # I1: 6,9 => CTR => I1: 1,5 * DIS # C2: 6,9 => CTR => C2: 1,3 * DIS # G2: 6,9 => CTR => G2: 1,2 * DIS # I2: 6,9 => CTR => I2: 1,3,8 * DIS # E4: 5 => CTR => E4: 6,9 * DIS # F9: 2,8 => CTR => F9: 6,9 * DIS # I1: 6,9 => CTR => I1: 1,5 * DIS # G2: 6,9 => CTR => G2: 1,2 * DIS # I2: 6,9 => CTR => I2: 1,3,8 * DIS # I3: 6,9 => CTR => I3: 3 * DIS # C3: 3 => CTR => C3: 6,9 * DIS # G5: 6,9 => CTR => G5: 5 * DIS # B5: 8,9 => CTR => B5: 1 * PRF # C6: 8,9 => SOL * DIS # B8: 7 => CTR => B8: 8,9 * DIS # E4: 5 => CTR => E4: 6,9 * DIS # E4: 5,9 => CTR => E4: 6 * PRF # E4: 6 => SOL * DIS # F7: 5,9 => CTR => F7: 2,8 * PRF # C5: 1,6,9 => SOL * PRF # C6: 2,8 => SOL * DIS # F7: 5,9 => CTR => F7: 2,8 * DIS # E4: 5,9 => CTR => E4: 6 * PRF # E4: 6 => SOL * DIS # H1: 5,6 => CTR => H1: 9 * PRF # H1: 9 => SOL * PRF # H6: 5,6 => SOL * DIS # H6: 9 => CTR => H6: 5,6 * DIS # F9: 2,8 => CTR => F9: 6,9 * CNT 30 HDP CHAINS / 71 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 6,9 => CTR => C1: 1 * DIS C1: 1 # I1: 6,9 => CTR => I1: 5 * DIS C1: 1 + I1: 5 # A2: 7 => CTR => A2: 6,9 * DIS C1: 1 + I1: 5 + A2: 6,9 # E4: 5 => CTR => E4: 6,9 * DIS C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 # F9: 2,8 => CTR => F9: 9 * PRF C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 # C6: 8,9 => SOL * STA C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 + C6: 8,9 * CNT 6 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 82..3.......5...4..........3.....8.2...4.7......1......64....7.....1.3....5...... | initial |
| 82..347.....5...4.45..71...347...812...4.7.3....1.34.7.643...7.....1.3.4.35.4.... | autosolve |
| 821634795673598241459271683347965812216487539598123467164352978982716354735849126 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) D1: 6,9 E2: 6,9 F2: 2,8 D3: 2,8 G3: 6,9 H3: 2,8 B6: 8,9 D4: 6,9 F4: 5,9 E5: 2,8 E6: 2,8 A7: 1,2 E7: 5,9 D8: 2,7 F8: 5,6 H8: 5,6 H9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 1.. / B5 = 1 => 20 pairs (_) / C5 = 1 => 0 pairs (X) A7,A9: 1.. / A7 = 1 => 19 pairs (_) / A9 = 1 => 17 pairs (_) C1,I1: 1.. / C1 = 1 => 21 pairs (_) / I1 = 1 => 0 pairs (X) B2,B5: 1.. / B2 = 1 => 0 pairs (X) / B5 = 1 => 20 pairs (_) F2,D3: 2.. / F2 = 2 => 16 pairs (_) / D3 = 2 => 19 pairs (_) G2,H3: 2.. / G2 = 2 => 19 pairs (_) / H3 = 2 => 16 pairs (_) E5,E6: 2.. / E5 = 2 => 0 pairs (X) / E6 = 2 => 16 pairs (_) F2,G2: 2.. / F2 = 2 => 16 pairs (_) / G2 = 2 => 19 pairs (_) D3,H3: 2.. / D3 = 2 => 19 pairs (_) / H3 = 2 => 16 pairs (_) H3,H9: 2.. / H3 = 2 => 16 pairs (_) / H9 = 2 => 19 pairs (_) C2,C3: 3.. / C2 = 3 => 18 pairs (_) / C3 = 3 => 0 pairs (X) I2,I3: 3.. / I2 = 3 => 0 pairs (X) / I3 = 3 => 18 pairs (_) C2,I2: 3.. / C2 = 3 => 18 pairs (_) / I2 = 3 => 0 pairs (X) C3,I3: 3.. / C3 = 3 => 0 pairs (X) / I3 = 3 => 18 pairs (_) H1,I1: 5.. / H1 = 5 => 0 pairs (X) / I1 = 5 => 23 pairs (_) A5,A6: 5.. / A5 = 5 => 0 pairs (X) / A6 = 5 => 18 pairs (_) E4,F4: 5.. / E4 = 5 => 0 pairs (X) / F4 = 5 => 21 pairs (_) A6,H6: 5.. / A6 = 5 => 18 pairs (_) / H6 = 5 => 0 pairs (X) F8,H8: 5.. / F8 = 5 => 0 pairs (X) / H8 = 5 => 22 pairs (_) E4,E7: 5.. / E4 = 5 => 0 pairs (X) / E7 = 5 => 21 pairs (_) G5,G7: 5.. / G5 = 5 => 19 pairs (_) / G7 = 5 => 0 pairs (X) D1,E2: 6.. / D1 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) D4,E4: 6.. / D4 = 6 => 0 pairs (X) / E4 = 6 => 0 pairs (_) F8,F9: 6.. / F8 = 6 => 22 pairs (_) / F9 = 6 => 0 pairs (X) F8,H8: 6.. / F8 = 6 => 22 pairs (_) / H8 = 6 => 0 pairs (X) D1,D4: 6.. / D1 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) E2,E4: 6.. / E2 = 6 => 0 pairs (X) / E4 = 6 => 0 pairs (_) A2,B2: 7.. / A2 = 7 => 0 pairs (X) / B2 = 7 => 21 pairs (_) D8,D9: 7.. / D8 = 7 => 23 pairs (_) / D9 = 7 => 18 pairs (_) A9,D9: 7.. / A9 = 7 => 23 pairs (_) / D9 = 7 => 18 pairs (_) B2,B8: 7.. / B2 = 7 => 21 pairs (_) / B8 = 7 => 0 pairs (X) F2,D3: 8.. / F2 = 8 => 19 pairs (_) / D3 = 8 => 16 pairs (_) I2,H3: 8.. / I2 = 8 => 16 pairs (_) / H3 = 8 => 19 pairs (_) E5,E6: 8.. / E5 = 8 => 16 pairs (_) / E6 = 8 => 0 pairs (X) B8,C8: 8.. / B8 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) F2,I2: 8.. / F2 = 8 => 19 pairs (_) / I2 = 8 => 16 pairs (_) D3,H3: 8.. / D3 = 8 => 16 pairs (_) / H3 = 8 => 19 pairs (_) F7,I7: 8.. / F7 = 8 => 16 pairs (_) / I7 = 8 => 19 pairs (_) D3,D9: 8.. / D3 = 8 => 16 pairs (_) / D9 = 8 => 19 pairs (_) H3,H9: 8.. / H3 = 8 => 19 pairs (_) / H9 = 8 => 16 pairs (_) D1,E2: 9.. / D1 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) D1,D4: 9.. / D1 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) H1,H6: 9.. / H1 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) * DURATION: 0:01:37.832437 START: 05:30:17.422848 END: 05:31:55.255285 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B6,D1,D3,D4,D8,E2,E5,E6,E7,F2,F4,F8,G3,H3,H8,H9) * 82..347.....5...4.45..71...347...812...4.7.3....1.34.7.643...7.....1.3.4.35.4.... * PAIR D1: 6,9 ROW 1 C1: 6,9,1 # reduction candidate for 6,9 C1: 6,9 => CTR * 82..34751...5...4.45..71...347.59812...4.7.3.586123497.6439..7...8.15364.35.46... C1: 1 # 21 pairs H1: 6,9,5 # reduction candidate for 6,9 H1: 6,9 # 23 pairs I1: 6,9,1,5 # reduction candidate for 6,9 I1: 6,9 => CTR * 8219347566..5...4.45..71...347.59812.1.4.7.3.586123497.6439..7...8.15364.35.46... I1: 1,5 # 18 pairs * PAIR E2: 6,9 ROW 2 A2: 6,9,7 # reduction candidate for 6,9 A2: 6,9 # 21 pairs C2: 6,9,1,3 # reduction candidate for 6,9 C2: 6,9 => CTR * 82..347.....5.8243453271.8.347...812...4.7.3....1.34.7.643.2.78...71.3.473584..2. C2: 1,3 # 18 pairs G2: 6,9,1,2 # reduction candidate for 6,9 G2: 6,9 => CTR * 82..34751.135.2.4845.871.23347...812..14.7.3.5..1.3497.643.8.7..78215364.35746.89 G2: 1,2 # 18 pairs I2: 6,9,1,3,8 # reduction candidate for 6,9 I2: 6,9 => CTR * 82..347....35.824.45.271.83347...812...4.7.3....1.34.7.643...78...71.3.473584..2. I2: 1,3,8 # 17 pairs * PAIR E2: 6,9 COL E E4: 6,9,5 # reduction candidate for 6,9 E4: 5 => CTR * 82.9347.....56..4.45..71...347659812...4.7.3.586123497.6439..7...8.1.3.4.35.4.... E4: 6,9 # 21 pairs * PAIR F2: 2,8 COL F F7: 2,8,5,9 # reduction candidate for 2,8 F7: 2,8 # 19 pairs F9: 2,8,6,9 # reduction candidate for 2,8 F9: 2,8 => CTR * 821.347.5..35...4145.871.2.347...812.1.4.753.5..1.34.7.643...7.....16354.35.4.... F9: 6,9 # 19 pairs * PAIR D3: 2,8 COL D D9: 2,8,7 # reduction candidate for 2,8 D9: 2,8 # 23 pairs D9: 7 # 18 pairs * PAIR G3: 6,9 BLK 3 H1: 6,9,5 # reduction candidate for 6,9 H1: 6,9 # 23 pairs I1: 6,9,1,5 # reduction candidate for 6,9 I1: 6,9 => CTR * 8219347566..5...4.45..71...347.59812.1.4.7.3.586123497.6439..7...8.15364.35.46... I1: 1,5 # 18 pairs G2: 6,9,1,2 # reduction candidate for 6,9 G2: 6,9 => CTR * 82..34751.135.2.4845.871.23347...812..14.7.3.5..1.3497.643.8.7..78215364.35746.89 G2: 1,2 # 18 pairs I2: 6,9,1,3,8 # reduction candidate for 6,9 I2: 6,9 => CTR * 82..347....35.824.45.271.83347...812...4.7.3....1.34.7.643...78...71.3.473584..2. I2: 1,3,8 # 17 pairs I3: 6,9,3 # reduction candidate for 6,9 I3: 6,9 => CTR * 82..34751.715.8243453271986347.59812.1.4.76355.6123497164392578.98715364735846129 I3: 3 # 18 pairs * PAIR G3: 6,9 ROW 3 C3: 6,9,3 # reduction candidate for 6,9 C3: 3 => CTR * 82..34751.715.8243453271986347.59812.1.4.76355.6123497164392578.98715364735846129 C3: 6,9 # 18 pairs * PAIR G3: 6,9 COL G G5: 6,9,5 # reduction candidate for 6,9 G5: 6,9 => CTR * 82.93475....56..4.45..71...347659812...4.7.355.6123497.6439.57.....15364.35.46... G5: 5 # 19 pairs G9: 6,9,1,2 # reduction candidate for 6,9 G9: 6,9 # 22 pairs * PAIR B6: 8,9 BLK 4 B5: 8,9,1 # reduction candidate for 8,9 B5: 8,9 => CTR * 82..347517135.2.4845.871.23347...812.81427.3.5921834.7.643.8.7.97821.3.4.3574..8. B5: 1 # 20 pairs C5: 8,9,1,2,6 # reduction candidate for 8,9 C5: 8,9 # 22 pairs C6: 8,9,2,6 # reduction candidate for 8,9 C6: 8,9 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 C6: 2,6 # 18 pairs * PAIR B6: 8,9 COL B B8: 8,9,7 # reduction candidate for 8,9 B8: 7 => CTR * 82..347957.3592.4845.871.23347...812...4.7.3....1.34.7.643.8.7.97821.3.4.3574..8. B8: 8,9 # 21 pairs * PAIR D4: 6,9 BLK 5 E4: 6,9,5 # reduction candidate for 6,9 E4: 5 => CTR * 82.9347.....56..4.45..71...347659812...4.7.3.586123497.6439..7...8.1.3.4.35.4.... E4: 6,9 # 21 pairs * PAIR F4: 5,9 BLK 5 E4: 5,9,6 # reduction candidate for 5,9 E4: 5,9 => CTR * 82.9347.....56..4.45..71...3476..812...4.7.3.586123497.643...7...8.1.3.4.35.4.... E4: 6 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 * PAIR F4: 5,9 COL F F7: 5,9,2,8 # reduction candidate for 5,9 F7: 5,9 => CTR * 82..347.....5...4.45..71...347...812...4.7.3....1.34.7.643...78....1.3.4.35.4..2. F7: 2,8 # 19 pairs * PAIR E5: 2,8 ROW 5 C5: 2,8,1,6,9 # reduction candidate for 2,8 C5: 1,6,9 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 C5: 2,8 # 21 pairs * PAIR E6: 2,8 ROW 6 C6: 2,8,6,9 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 C6: 6,9 # 23 pairs * PAIR A7: 1,2 BLK 7 A9: 1,2,7 # reduction candidate for 1,2 A9: 7 # 23 pairs A9: 1,2 # 18 pairs * PAIR A7: 1,2 ROW 7 G7: 1,2,5,9 # reduction candidate for 1,2 G7: 5,9 # 26 pairs G7: 1,2 # 20 pairs * PAIR E7: 5,9 BLK 8 F7: 5,9,2,8 # reduction candidate for 5,9 F7: 5,9 => CTR * 82..347.....5...4.45..71...347...812...4.7.3....1.34.7.643...78....1.3.4.35.4..2. F7: 2,8 # 19 pairs * PAIR E7: 5,9 ROW 7 G7: 5,9,1,2 # reduction candidate for 5,9 G7: 5,9 # 26 pairs I7: 5,9,1,8 # reduction candidate for 5,9 I7: 5,9 # 20 pairs * PAIR E7: 5,9 COL E E4: 5,9,6 # reduction candidate for 5,9 E4: 5,9 => CTR * 82.9347.....56..4.45..71...3476..812...4.7.3.586123497.643...7...8.1.3.4.35.4.... E4: 6 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 * PAIR D8: 2,7 BLK 8 D9: 2,7,8 # reduction candidate for 2,7 D9: 8 # 19 pairs D9: 2,7 # 16 pairs * PAIR D8: 2,7 ROW 8 A8: 2,7,9 # reduction candidate for 2,7 A8: 2,7 # 24 pairs A8: 9 # 20 pairs * PAIR H8: 5,6 COL H H1: 5,6,9 # reduction candidate for 5,6 H1: 5,6 => CTR * 82..347..67.59..4.45..71...347965812.12487.3.586123497.6435..7..98.16354.35.4.... H1: 9 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 H6: 5,6,9 # reduction candidate for 5,6 H6: 5,6 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 H6: 9 => CTR * 82..347..67.59..4.45..71...347965812.1.487.3.586123497.6435..7..98.16354.35.4.... * PAIR H9: 2,8 ROW 9 D9: 2,8,7 # reduction candidate for 2,8 D9: 2,8 # 23 pairs F9: 2,8,6,9 # reduction candidate for 2,8 F9: 2,8 => CTR * 821.347.5..35...4145.871.2.347...812.1.4.753.5..1.34.7.643...7.....16354.35.4.... F9: 6,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-080-base-pr-000.dot * REASONING * DIS # C1: 6,9 => CTR => C1: 1 * DIS # I1: 6,9 => CTR => I1: 1,5 * DIS # C2: 6,9 => CTR => C2: 1,3 * DIS # G2: 6,9 => CTR => G2: 1,2 * DIS # I2: 6,9 => CTR => I2: 1,3,8 * DIS # E4: 5 => CTR => E4: 6,9 * DIS # F9: 2,8 => CTR => F9: 6,9 * DIS # I1: 6,9 => CTR => I1: 1,5 * DIS # G2: 6,9 => CTR => G2: 1,2 * DIS # I2: 6,9 => CTR => I2: 1,3,8 * DIS # I3: 6,9 => CTR => I3: 3 * DIS # C3: 3 => CTR => C3: 6,9 * DIS # G5: 6,9 => CTR => G5: 5 * DIS # B5: 8,9 => CTR => B5: 1 * PRF # C6: 8,9 => SOL * DIS # B8: 7 => CTR => B8: 8,9 * DIS # E4: 5 => CTR => E4: 6,9 * DIS # E4: 5,9 => CTR => E4: 6 * PRF # E4: 6 => SOL * DIS # F7: 5,9 => CTR => F7: 2,8 * PRF # C5: 1,6,9 => SOL * PRF # C6: 2,8 => SOL * DIS # F7: 5,9 => CTR => F7: 2,8 * DIS # E4: 5,9 => CTR => E4: 6 * PRF # E4: 6 => SOL * DIS # H1: 5,6 => CTR => H1: 9 * PRF # H1: 9 => SOL * PRF # H6: 5,6 => SOL * DIS # H6: 9 => CTR => H6: 5,6 * DIS # F9: 2,8 => CTR => F9: 6,9 * CNT 30 HDP CHAINS / 71 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B6,D1,D3,D4,D8,E2,E5,E6,E7,F2,F4,F8,G3,H3,H8,H9) * 82..347.....5...4.45..71...347...812...4.7.3....1.34.7.643...7.....1.3.4.35.4.... * PAIR D1: 6,9 ROW 1 C1: 6,9,1 # reduction candidate for 6,9 C1: 6,9 => CTR * 82..34751...5...4.45..71...347.59812...4.7.3.586123497.6439..7...8.15364.35.46... H1: 6,9,5 # reduction candidate for 6,9 H1: 6,9 # 23 pairs I1: 6,9,5 # reduction candidate for 6,9 I1: 6,9 => CTR * 821934756..35...4.45..71..3347.59812.1.4.7.3.586123497.6439..7...8.15364.35.46... * RESTART * PAIR RESTART * PAIR E2: 6,9 ROW 2 A2: 6,9,7 # reduction candidate for 6,9 A2: 7 => CTR * 821.347.579356..4.456.719.33476..812.1.4.7.3..8.123497.643...7.....1.3.4.35.4.... * PAIR E2: 6,9 COL E E4: 6,9,5 # reduction candidate for 6,9 E4: 5 => CTR * 821.347.5.7356..4.456.719.3347659812.1.4.7.3....1.3497.6439..7..98.1.354.35.4...9 * PAIR RESTART * PAIR F2: 2,8 COL F F7: 2,8,9 # reduction candidate for 2,8 F7: 2,8 # 23 pairs F9: 2,8,9 # reduction candidate for 2,8 F9: 2,8 => CTR * 821.347.5.735...4.45..71..3347..5812.1.4.753.5..1.34.7.64359.78....16354.35.4..2. * RESTART * PAIR RESTART * PAIR D3: 2,8 COL D D9: 2,8,7 # reduction candidate for 2,8 D9: 2,8 # 27 pairs D9: 7 # 23 pairs * PAIR B6: 8,9 BLK 4 C5: 8,9,2,6 # reduction candidate for 8,9 C5: 8,9 # 26 pairs C6: 8,9,2,6 # reduction candidate for 8,9 C6: 8,9 => SOLVED * 821634795673598241459271683347965812216487539598123467164352978982716354735849126 * DURATION: 0:00:20.119480 START: 05:33:21.802866 END: 05:33:41.922346 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-080-base-pr-001.dot * REASONING * DIS # C1: 6,9 => CTR => C1: 1 * DIS C1: 1 # I1: 6,9 => CTR => I1: 5 * DIS C1: 1 + I1: 5 # A2: 7 => CTR => A2: 6,9 * DIS C1: 1 + I1: 5 + A2: 6,9 # E4: 5 => CTR => E4: 6,9 * DIS C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 # F9: 2,8 => CTR => F9: 9 * PRF C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 # C6: 8,9 => SOL * STA C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 + C6: 8,9 * CNT 6 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 080 solution: 821634795673598241459271683347965812216487539598123467164352978982716354735849126 info: 1524 FNBTHWXY S8.f 38654 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 821634795673598241459271683347965812216487539598123467164352978982716354735849126 solved
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:
* DIS # C1: 6,9 => CTR => C1: 1 * INC # C1: 1 => UNS * INC # H1: 6,9 => UNS * DIS # I1: 6,9 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * INC # A2: 6,9 => UNS * DIS # C2: 6,9 => CTR => C2: 1,3 * INC # C2: 1,3 => UNS * DIS # G2: 6,9 => CTR => G2: 1,2 * INC # G2: 1,2 => UNS * DIS # I2: 6,9 => CTR => I2: 1,3,8 * INC # I2: 1,3,8 => UNS * INC # E4: 6,9 => UNS * DIS # E4: 5 => CTR => E4: 6,9 * INC # F7: 2,8 => UNS * DIS # F9: 2,8 => CTR => F9: 6,9 * INC # F9: 6,9 => UNS * INC # D9: 2,8 => UNS * INC # D9: 7 => UNS * INC # H1: 6,9 => UNS * DIS # I1: 6,9 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * DIS # G2: 6,9 => CTR => G2: 1,2 * INC # G2: 1,2 => UNS * DIS # I2: 6,9 => CTR => I2: 1,3,8 * INC # I2: 1,3,8 => UNS * DIS # I3: 6,9 => CTR => I3: 3 * INC # I3: 3 => UNS * INC # C3: 6,9 => UNS * DIS # C3: 3 => CTR => C3: 6,9 * DIS # G5: 6,9 => CTR => G5: 5 * INC # G5: 5 => UNS * INC # G9: 6,9 => UNS * DIS # B5: 8,9 => CTR => B5: 1 * INC # B5: 1 => UNS * INC # C5: 8,9 => UNS * PRF # C6: 8,9 => SOL * INC # C6: 2,6 => UNS * INC # B8: 8,9 => UNS * DIS # B8: 7 => CTR => B8: 8,9 * INC # E4: 6,9 => UNS * DIS # E4: 5 => CTR => E4: 6,9 * DIS # E4: 5,9 => CTR => E4: 6 * PRF # E4: 6 => SOL * DIS # F7: 5,9 => CTR => F7: 2,8 * INC # F7: 2,8 => UNS * INC # C5: 2,8 => UNS * PRF # C5: 1,6,9 => SOL * PRF # C6: 2,8 => SOL * INC # C6: 6,9 => UNS * INC # A9: 1,2 => UNS * INC # A9: 7 => UNS * INC # G7: 1,2 => UNS * INC # G7: 5,9 => UNS * DIS # F7: 5,9 => CTR => F7: 2,8 * INC # F7: 2,8 => UNS * INC # G7: 5,9 => UNS * INC # I7: 5,9 => UNS * DIS # E4: 5,9 => CTR => E4: 6 * PRF # E4: 6 => SOL * INC # D9: 2,7 => UNS * INC # D9: 8 => UNS * INC # A8: 2,7 => UNS * INC # A8: 9 => UNS * DIS # H1: 5,6 => CTR => H1: 9 * PRF # H1: 9 => SOL * PRF # H6: 5,6 => SOL * DIS # H6: 9 => CTR => H6: 5,6 * INC # D9: 2,8 => UNS * DIS # F9: 2,8 => CTR => F9: 6,9 * INC # F9: 6,9 => UNS * CNT 71 HDP CHAINS / 71 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 6,9 => CTR => C1: 1 * INC C1: 1 # H1: 6,9 => UNS * DIS C1: 1 # I1: 6,9 => CTR => I1: 5 * INC C1: 1 + I1: 5 # A2: 6,9 => UNS * DIS C1: 1 + I1: 5 # A2: 7 => CTR => A2: 6,9 * INC C1: 1 + I1: 5 + A2: 6,9 # E4: 6,9 => UNS * DIS C1: 1 + I1: 5 + A2: 6,9 # E4: 5 => CTR => E4: 6,9 * INC C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 # F7: 2,8 => UNS * DIS C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 # F9: 2,8 => CTR => F9: 9 * INC C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 # D9: 2,8 => UNS * INC C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 # D9: 7 => UNS * INC C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 # C5: 8,9 => UNS * PRF C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 # C6: 8,9 => SOL * STA C1: 1 + I1: 5 + A2: 6,9 + E4: 6,9 + F9: 9 + C6: 8,9 * CNT 13 HDP CHAINS / 13 HYP OPENED