#71 ⟨a, b | ababba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 6
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = db
- b-1 = ad
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aabab-1⟩
- Isomorphism: φ(a) = b-1a, φ(b) = b
- Auxiliary generators:
- c = ba
- d = bca
- Reduction order:
- Right-to-left recursive path with deg(d) = deg(c) = 0, d < c; deg(b) = 1; deg(a) = 2
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:ababba=1 reversed:dc/b/a ba=c,bca=d morph:2/0,3/0
cd=1
dc=1
bd=ccb
bc=ddb
ba=c
ac=dad
add=ca
adb=1
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 5 | 39 | ⟨a, b | aaba=b⟩ | Infinite cancellative non-commutative monoid | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 6 | 72 | ⟨a, b | abbaab=1⟩ | φ(a) = adba, φ(b) = b |
| 9 | 660 | ⟨a, b | aabaababa=1⟩ | φ(a) = ad, φ(b) = bbab |
| 9 | 665 | ⟨a, b | aababaaab=1⟩ | φ(a) = ad, φ(b) = bbba |
| 9 | 666 | ⟨a, b | aababaaba=1⟩ | φ(a) = b, φ(b) = adbaad |
| 9 | 699 | ⟨a, b | abaaabaab=1⟩ | φ(a) = ad, φ(b) = bbba |
| 9 | 700 | ⟨a, b | abaaababa=1⟩ | φ(a) = b, φ(b) = adbaad |
| 9 | 703 | ⟨a, b | abaabaaab=1⟩ | φ(a) = b, φ(b) = adadba |