| Up: | Monoids with two generators and two relations |
|---|---|
| Prev: | #1693 ⟨a, b | abb=bb, bbb=b⟩ |
| Next: | #1697 ⟨a, b | bab=ab, bbb=b⟩ |
| index 1, period 1 | 2 elements | b2, (ab2)3 |
| index 1, period 2 | 4 elements | b, b(ab2)2, (b2a)2b, a(b2a)2b |
| index 1, period 3 | 2 elements | (bab)2, b2(ab2)2 |
| index 2, period 1 | 2 elements | (ab)2, a(b2a)2 |
| index 2, period 2 | 3 elements | abab2, ab2ab, bab2a |
| index 2, period 3 | 5 elements | bab, ab2a, b2ab2, (ab2)2, (b2a)2 |
| index 3, period 2 | 5 elements | ab, ba, aba, bab2, b2ab |
| index 3, period 3 | 2 elements | ab2, b2a |
| index 4, period 3 | 1 element | a |
| # | Rule | Proof |
|---|---|---|
| 1. | b3 ⇒ b | [2] |
| 2. | a2 ⇒ bab | [1] |
| 3. | (ba)2 ⇒ (ab)2 | [3] |
| 4. | abab2a ⇒ (b2a)2b | [4] |
| 5. | ba(b2a)2 ⇒ a(b2a)2b | [5] |
# ab:bab=aa,bbb=b b/a bbb=b aa=bab baba=abab ababba=bbabbab babbabba=abbabbab
| Σ | # | Presentation | Description | Related |
|---|---|---|---|---|
| 8 | 450 | ⟨a, b | bab=aa, bbb=1⟩ | Finite non-commutative monoid with 27 elements | 27 iso |
| 8 | 752 | ⟨a, b | aaa=1, babb=a⟩ | Finite non-Abelian group with 27 elements | 59 iso |
| 10 | 5300 | ⟨a, b | aaa=aa, aba=bb⟩ | Finite non-commutative monoid with 27 elements | |
| 11 | 15514 | ⟨a, b | aaa=bb, aabaa=b⟩ | Finite non-commutative monoid with 27 elements | |
| 11 | 18739 | ⟨a, b | aaa=a, abbbbb=b⟩ | Finite non-commutative monoid with 27 elements | |
| 11 | 20314 | ⟨a, b | aba=b, bbbb=aaa⟩ | Finite non-commutative monoid with 27 elements |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 11 | 19242 | ⟨a, b | aaa=a, aaaba=bb⟩ | φ(a) = b, φ(b) = a |