# exhaust.c (plain enumeration) and exhaust2.c (structured, symmetry-reduced); compiled with cc -O2
$ exhaust 8 3
n=8 k=3 pairs=16 tested=560 successes=0  => no R of this size
$ exhaust 8 4
example: 0-3 0-5 0-6 1-2
example: 0-3 0-5 0-6 1-4
example: 0-3 0-5 0-6 2-4
n=8 k=4 pairs=16 tested=1820 successes=768  => wsat <= 11+k
$ exhaust 9 4
n=9 k=4 pairs=24 tested=4326 successes=0  => no R of this size
$ exhaust 9 5
example: 0-3 0-5 0-8 1-2 2-8
example: 0-3 0-5 0-8 1-2 3-8
example: 0-3 0-5 0-8 1-2 4-8
n=9 k=5 pairs=24 tested=23576 successes=6864  => wsat <= 11+k
$ exhaust 10 5
n=10 k=5 pairs=33 tested=32208 successes=0  => no R of this size
$ exhaust 10 6
n=10 k=6 pairs=33 tested=272048 successes=0  => no R of this size
$ exhaust 10 7
example: 0-3 0-5 0-8 0-9 1-2 1-8 2-9
example: 0-3 0-5 0-8 0-9 1-2 1-8 3-9
example: 0-3 0-5 0-8 0-9 1-2 1-8 4-9
n=10 k=7 pairs=33 tested=1584240 successes=554712  => wsat <= 11+k
$ exhaust 11 7
n=11 k=7 pairs=43 tested=3116702 successes=0  => no R of this size
$ exhaust 11 8  (run earlier, saved output)
example: 0-3 0-5 1-8 2-9 2-10 3-9 5-10 8-9
example: 0-3 0-5 1-8 2-9 2-10 3-9 5-10 8-10
example: 0-3 0-5 1-8 2-9 2-10 3-9 8-9 8-10
n=11 k=8 pairs=43 tested=25547880 successes=428832  => wsat <= 11+k
$ exhaust2 8 3
n=8 k=3 outside-configs=1 tested=560 successes=0 => no R of this size (wsat >= 12+k)
$ exhaust2 8 4
example R: 0-3 0-5 0-6 1-2
example R: 0-3 0-5 0-6 1-4
example R: 0-3 0-5 0-6 2-4
n=8 k=4 outside-configs=1 tested=1820 successes=768 => wsat <= 11+k
$ exhaust2 9 4
n=9 k=4 outside-configs=154 tested=4326 successes=0 => no R of this size (wsat >= 12+k)
$ exhaust2 9 5
example R: 0-3 0-6 0-8 1-2 1-8
example R: 0-3 0-6 0-8 1-4 1-8
example R: 0-3 0-6 0-8 1-7 1-8
n=9 k=5 outside-configs=210 tested=23576 successes=6864 => wsat <= 11+k
$ exhaust2 10 6
n=10 k=6 outside-configs=11032 tested=172984 successes=0 => no R of this size (wsat >= 12+k)
$ exhaust2 10 7
example R: 0-3 0-6 0-8 0-9 1-2 1-8 1-9
example R: 0-3 0-6 0-8 0-9 1-4 1-8 1-9
example R: 0-3 0-6 0-8 0-9 1-7 1-8 1-9
n=10 k=7 outside-configs=22064 tested=1027096 successes=380184 => wsat <= 11+k
$ exhaust2 11 7
n=11 k=7 outside-configs=194848 tested=884272 successes=0 => no R of this size (wsat >= 12+k)
$ exhaust2 11 8 stop
example R: 0-8 0-9 1-9 3-5 3-10 4-10 8-9 8-10
n=11 k=8 stopped at first success
$ exhaust2 12 10 stop
example R: 0-9 0-10 0-11 1-4 1-9 2-4 2-10 8-9 8-10 8-11
n=12 k=10 stopped at first success
$ exhaust2 12 9  (run earlier, saved output, about 2 minutes)
n=12 k=9 outside-configs=11553698 tested=51502128 successes=0 => no R of this size (wsat >= 12+k)
$ exhaust2 13 10  (run 2026-10-19, wall time from /usr/bin/time)
n=13 k=10 outside-configs=130033860 tested=270778851 successes=0 => no R of this size (wsat >= 12+k)
real 726.62
user 724.60
sys 1.31
