#936 ⟨a, b | ab=a, baaa=a⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 8
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Commutative Gröbner basis: ⟨a, b | ab=a, a3=a⟩
- Cancellative quotient is isomorphic to ℤ2
- Enveloping group is isomorphic to ℤ2
- Group of units is isomorphic to ℤ1
- 3 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,baaa=a ab
ab=a
ba=a
aaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
55 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2970 | ⟨a, b | ab=a, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2972 | ⟨a, b | ab=a, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 2976 | ⟨a, b | ab=a, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3105 | ⟨a, b | ab=a, baaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 5110 | ⟨a, b | aab=aa, baaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5173 | ⟨a, b | aab=ba, abbb=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 5257 | ⟨a, b | aba=ab, abbb=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 8782 | ⟨a, b | ab=a, baaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8786 | ⟨a, b | ab=a, baabab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8788 | ⟨a, b | ab=a, baabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8794 | ⟨a, b | ab=a, babaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8796 | ⟨a, b | ab=a, bababa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8800 | ⟨a, b | ab=a, babbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 9053 | ⟨a, b | ab=a, baaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9057 | ⟨a, b | ab=a, baaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9065 | ⟨a, b | ab=a, babaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9323 | ⟨a, b | ab=a, baaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 12270 | ⟨a, b | aaab=ba, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12274 | ⟨a, b | aaab=ba, abaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12282 | ⟨a, b | aaab=ba, baaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12362 | ⟨a, b | aaba=ab, baaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12492 | ⟨a, b | abaa=ab, baaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14443 | ⟨a, b | aaab=a, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14445 | ⟨a, b | aaab=a, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14449 | ⟨a, b | aaab=a, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14571 | ⟨a, b | aaba=a, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15579 | ⟨a, b | aab=aa, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15581 | ⟨a, b | aab=aa, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15585 | ⟨a, b | aab=aa, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15638 | ⟨a, b | aab=ab, abbba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15700 | ⟨a, b | aab=ba, abbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15829 | ⟨a, b | aba=aa, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15864 | ⟨a, b | aba=ab, ababb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15868 | ⟨a, b | aba=ab, abbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15870 | ⟨a, b | aba=ab, abbba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 24474 | ⟨a, b | ab=a, baaabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24482 | ⟨a, b | ab=a, baababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24486 | ⟨a, b | ab=a, baabbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24488 | ⟨a, b | ab=a, baabbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24498 | ⟨a, b | ab=a, babaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24502 | ⟨a, b | ab=a, bababab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24504 | ⟨a, b | ab=a, bababba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24510 | ⟨a, b | ab=a, babbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24512 | ⟨a, b | ab=a, babbaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24516 | ⟨a, b | ab=a, babbbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 25001 | ⟨a, b | ab=a, baaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25009 | ⟨a, b | ab=a, baabab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25013 | ⟨a, b | ab=a, baabba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25025 | ⟨a, b | ab=a, babaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25029 | ⟨a, b | ab=a, bababa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25037 | ⟨a, b | ab=a, babbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25543 | ⟨a, b | ab=a, baaab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25551 | ⟨a, b | ab=a, baaba=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25567 | ⟨a, b | ab=a, babaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25827 | ⟨a, b | ab=a, baaa=abbb⟩ | φ(a) = a, φ(b) = b |