#1592 ⟨a, b | aaa=ab, baa=a⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 9
- Infinite non-cancellative commutative monoid
- Not cancellative, because multiplication by a3 is not injective:
-
a3 ⋅ b2 = a and a3 ⋅ a = a, however b2 ≠ a
- Commutative Gröbner basis: ⟨a, b | a4=a, ab=a3⟩
- Cancellative quotient is isomorphic to ℤ3
- Enveloping group is isomorphic to ℤ3
- Group of units is isomorphic to ℤ1
- 3 Archimedian components:
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=ab,baa=a a/b
aaaa=a
ba=aaa
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
39 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 1679 | ⟨a, b | aba=bb, abb=b⟩ | φ(a) = b, φ(b) = a |
| 9 | 1683 | ⟨a, b | aba=bb, bab=b⟩ | φ(a) = b, φ(b) = a |
| 9 | 2042 | ⟨a, b | aab=a, babb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5279 | ⟨a, b | aba=bb, aaba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 12464 | ⟨a, b | aabb=ab, babb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12470 | ⟨a, b | aabb=ba, abaa=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 12539 | ⟨a, b | abab=ba, babb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12542 | ⟨a, b | abab=ba, bbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12576 | ⟨a, b | abba=ab, babb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12620 | ⟨a, b | baab=ab, bbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18896 | ⟨a, b | aab=a, baaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18910 | ⟨a, b | aab=a, baabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18918 | ⟨a, b | aab=a, bababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18922 | ⟨a, b | aab=a, babbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 18924 | ⟨a, b | aab=a, babbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19150 | ⟨a, b | aba=a, babbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 19382 | ⟨a, b | aab=a, aaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19386 | ⟨a, b | aab=a, aaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19394 | ⟨a, b | aab=a, aabaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19410 | ⟨a, b | aab=a, abaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19438 | ⟨a, b | aab=a, abbbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19441 | ⟨a, b | aab=a, baaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19452 | ⟨a, b | aab=a, baabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19460 | ⟨a, b | aab=a, babab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19464 | ⟨a, b | aab=a, babba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19469 | ⟨a, b | aab=a, babbb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19637 | ⟨a, b | aba=a, aaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19691 | ⟨a, b | aba=a, babab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19924 | ⟨a, b | aab=a, aaaa=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19933 | ⟨a, b | aab=a, aaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19941 | ⟨a, b | aab=a, aaba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19957 | ⟨a, b | aab=a, abaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 19980 | ⟨a, b | aab=a, abbb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19987 | ⟨a, b | aab=a, baaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 19992 | ⟨a, b | aab=a, baab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20000 | ⟨a, b | aab=a, baba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20009 | ⟨a, b | aab=a, babb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20010 | ⟨a, b | aab=a, babb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20195 | ⟨a, b | aba=a, aaba=bab⟩ | φ(a) = a, φ(b) = b |