Chord set validation:
  K9_CHORDS_3 (k=9): face sizes [2, 2, 2, 3]  OK
  K9_CHORDS_NESTED (k=9): face sizes [2, 2, 2, 3]  OK
  K12_CHORDS_3 (k=12): face sizes [3, 3, 3, 3]  OK
  K12_CHORDS_NESTED (k=12): face sizes [2, 2, 2, 3, 3]  OK

### Step 2 at k = 9

 γ  T1 (m_1, chords_1, model)               T2 (k_2, chords_2, model)                |S1|   |S2|     3^γ    fwd    rev  compat?  time
-----------------------------------------------------------------------------------------------------------------------------------------------
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (9, [(0, 2), (3, 5), (6, 8)], SP)        1296   7866   19683   1188    858      YES    0.2s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (9, [(0, 2), (4, 6), (3, 7)], SP)        1296   7536   19683   1242   1110      YES    0.2s
 9  (9, [(0, 2), (4, 6), (3, 7)], SP)       (9, [(0, 2), (4, 6), (3, 7)], SP)        1296   7536   19683   1176   1224      YES    0.2s
 9  (12, [(0, 2), (3, 5), (6, 8)], SP)      (9, [(0, 2), (3, 5), (6, 8)], SP)        1296   7866   19683   1188    858      YES    1.4s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (12, [(0, 3), (4, 7), (8, ..., SP)       1296   1302   19683     72     90      YES    0.6s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (12, [(0, 3), (4, 11), (5,..., SP)       1296   9456   19683    840    606      YES    0.7s
 9  (9, [(0, 2), (3, 5), (6, 8)], SR)       (9, [(0, 2), (3, 5), (6, 8)], SP)       19683   7866   19683   7866   7866      YES    1.2s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (3, —, SR)                               1296   3681   19683    108    108      YES    0.1s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (4, [(0, 2)], SP)                        1296   3162   19683    276    108      YES    0.1s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (6, [(0, 3)], SP)                        1296    942   19683     54     60      YES    0.1s
 9  (9, [(0, 2), (3, 5), (6, 8)], SP)       (6, [(0, 2), (3, 5)], SP)                1296   6210   19683    402    324      YES    0.2s
 9  (9, [(0, 2), (4, 6), (3, 7)], SP)       (6, [(0, 3)], SP)                        1296    942   19683     54     36      YES    0.1s
 9  (9, [(0, 2), (4, 6), (3, 7)], SP)       (12, [(0, 3), (4, 11), (5,..., SP)       1296   9456   19683    732    768      YES    0.8s

13/13 compatible at this k.

### Step 2 at k = 12

 γ  T1 (m_1, chords_1, model)               T2 (k_2, chords_2, model)                |S1|   |S2|     3^γ    fwd    rev  compat?  time
-----------------------------------------------------------------------------------------------------------------------------------------------
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (12, [(0, 3), (4, 7), (8, ..., SP)       1296  12840  531441    960    564      YES   11.3s
12  (12, [(0, 3), (4, 11), (5,..., SP)      (12, [(0, 3), (4, 11), (5,..., SP)       7776  100938  531441   5928   3414      YES   14.4s
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (12, [(0, 3), (4, 11), (5,..., SP)       1296  100938  531441   1128    912      YES   13.4s
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (3, —, SR)                               1296  31176  531441    192    192      YES    5.5s
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (4, [(0, 2)], SP)                        1296  27378  531441     48     60      YES    5.5s
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (6, [(0, 3)], SP)                        1296   9882  531441      6      6      YES    5.4s
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (6, [(0, 2), (3, 5)], SP)                1296  61224  531441     12     12      YES    5.8s
12  (12, [(0, 3), (4, 7), (8, ..., SP)      (9, [(0, 2), (3, 5), (6, 8)], SP)        1296  94116  531441     18     90      YES    6.7s
12  (12, [(0, 3), (4, 11), (5,..., SP)      (9, [(0, 2), (3, 5), (6, 8)], SP)        7776  94116  531441    552    852      YES    8.5s
12  (12, [(0, 3), (4, 7), (8, ..., SR)      (12, [(0, 3), (4, 7), (8, ..., SP)      531441  12840  531441  12840  12840      YES  143.9s

10/10 compatible at this k.

Total: 23/23 compatible across k=9 and k=12.
