#1328 ⟨a, b | aaaabbabba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = d2a3
- b-1 = bcda
- c-1 = d2
- d-1 = cd
- Reduced group presentation: ⟨a, b | aaaaabbabb⟩
- Isomorphism: φ(a) = a, φ(b) = b
- Auxiliary generators:
- c = aaaa
- d = abb
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaaabbabba=1 cda/b aaaa=c,abb=d morph:4/0,3/0
dc=cd
ac=ca
cdd=1
add=dda
aaaa=c
ab=dbcda
aaadb=cbddaaad
bb=ddaaad
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 10 | 2588 | ⟨a, b | abaaba=bbbb⟩ | Infinite cancellative non-commutative monoid | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1375 | ⟨a, b | aaabbabbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1470 | ⟨a, b | aabbbbbaab=1⟩ | φ(a) = b, φ(b) = a |
| 10 | 1504 | ⟨a, b | abaabbbbba=1⟩ | φ(a) = b, φ(b) = a |