Table 12.

Matrix decomposition table with topmost layer extracted from Table 11.

i	Coding	Reachable set R(Si)	Antecedent set Q(Si)	Collective set R(Si) $\cap$ Q(Si)
1	T1	4 5 15 18 20 excluded	1	1
2	T2	2 6 10 12	1 2 3 5 7 8 9 13 14 16 17	2
3	T3	1 4 5 8 14 15 18 20 excluded	1 3 5 7 8 9 13 14 16 17	3 7 9 13 16 17
4	T4	4	4 5	4
5	T5	8 14 15 18 20 excluded	5	5
6	T6	6	1 2 3 6–9 13 14 16 17	6
7	T7	2 3 6 7 9–13 16 17 19	1 3 5 7 8 9 13 14 16 17	3 7 9 13 16 17
8	O1	1 4 5 15 18 20 excluded	1 8 9 14	8 9 14
9	O2	1 4 5 15 18 20 excluded	3 5 7 8 9 13 14 16 17	3 7 8 9 13 14 16 17
10	O3	10	1 2 3 5 7–10 13 14 16 17	10
11	O4	11	1 3 5 7 8 9 11 13 14 16 17	11
12	O5	12	1 2 3 5 7 8 9 12 13 14 16 17	12
13	O6	1 4 5 14 15 18 20 excluded	1 3 5 7 8 9 13 14 16 17	3 7 8 9 13 16 17
14	E1	1 4 5 15 18 20 excluded	1 8 14	8 14
16	E3	1 4 5 8 14 15 18 20 excluded	1 3 5 7 8 9 13 14 16 17	3 7 9 13 16 17
17	E4	1 4 5 8 14 15 18 20 excluded	1 3 5 7 8 9 13 14 16 17	3 7 9 13 16 17
19	E6	19	1 3 5 7–9 13 14 16 17 19	19