| Up: | Monoid enumeration |
|---|---|
| Prev: | #12631 ⟨a, b | baba=ba, bbaa=a⟩ |
| Next: | #12635 ⟨a, b | babb=ab, bbbb=b⟩ |
| index 1, period 1 | 2 elements | b3, a(bab2)3 |
| index 1, period 3 | 16 elements | b, b2, bab3ab, abab3ab, b(ab3)2, ... |
| index 1, period 7 | 6 elements | (bab2)2, (b2ab)2, a(bab2)2, b3(ab3)2, (ab3)3, ... |
| index 2, period 1 | 2 elements | (ab)3, ab(ba)2b3a |
| index 2, period 3 | 22 elements | (ab)2, (ba)2, a(ba)2, abab3, (ab2)2, ... |
| index 2, period 7 | 15 elements | bab2, b2ab, abab2, ab2ab, ab3a, ... |
| index 3, period 7 | 2 elements | ab3, b3a |
| index 4, period 3 | 12 elements | ab, ba, aba, ab2, bab, ... |
| index 4, period 7 | 1 element | a |
| # | Rule | Proof |
|---|---|---|
| 1. | b4 ⇒ b | [2] |
| 2. | a2 ⇒ bab2 | [1] |
| 3. | bab2a ⇒ abab2 | [3] |
| 4. | b3(ab)2 ⇒ (ab)2 | [6] |
| 5. | (ab)3b2 ⇒ a(ba)2 | [10] |
| 6. | a(b2ab)2 ⇒ b3(ab3)2 | [7] |
| 7. | (ba)3 ⇒ (ab)3 | [11] |
| 8. | (ba)2b3ab ⇒ (ab3)3 | [14] |
| 9. | bab3aba ⇒ b2(ab3)2 | [9] |
| 10. | b(ab3)3 ⇒ ba(b3a)2 | [12] |
| 11. | b2a(b3a)2 ⇒ abab3ab | [13] |
# ab:babb=aa,bbbb=b b/a - - bbbb=b aa=babb babba=ababb bbbabab=abab abababbb=ababa abbabbbab=bbbabbbabbb bababa=ababab bababbbab=abbbabbbabbb babbbaba=bbabbbabbb babbbabbbabbb=babbbabbba bbabbbabbba=ababbbab