#315 ⟨a, b | aabbabba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 8
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = ac2
- b-1 = cadb
- c-1 = cd
- d-1 = c2
- Reduced group presentation: ⟨a, b | aaabbabb⟩
- Isomorphism: φ(a) = a, φ(b) = b
- Auxiliary generators:
- c = abb
- d = aa
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = deg(b) = 1, a < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aabbabba=1 cd/ab abb=c,aa=d morph:3/0,2/0
dc=cd
ccd=1
da=ad
cca=acc
aa=d
ba=acccbcdd
bca=cadbcc
bb=accc
3 unique, 3 total
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 316 | ⟨a, b | aabbbaab=1⟩ | φ(a) = b, φ(b) = a |
| 8 | 328 | ⟨a, b | abaabbba=1⟩ | φ(a) = b, φ(b) = a |