#1513 ⟨a, b | ababababba=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 = db
- b-1 = ad
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aaaabab-1⟩
- Isomorphism: φ(a) = b-1a, φ(b) = b
- Auxiliary generators:
- c = ba
- d = acccb
- Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(c) = 1; deg(a) = deg(b) = 2, a < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:ababababba=1 d/c/ab ba=c,acccb=d morph:2/0,5/0
cd=1
dc=1
da=acccc
ca=adddd
ddddb=bc
cb=dddbd
adb=1
ba=c
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 7 | 166 | ⟨a, b | aaaaba=b⟩ | Infinite cancellative non-commutative monoid | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1514 | ⟨a, b | abababbaab=1⟩ | φ(a) = adba, φ(b) = b |
| 10 | 1518 | ⟨a, b | ababbaabab=1⟩ | φ(a) = adba, φ(b) = b |