#2875 ⟨a, b | aaaabbaabba=1⟩
Quick links
- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 11
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = d2a2
- b-1 = bcda2
- c-1 = d2
- d-1 = cd
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generators:
- aaa=c
- aabb=d
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaaabbaabba=1 cda/b aaa=c,aabb=d morph:3/0,4/0
dc=cd
ac=ca
cdd=1
add=dda
aaa=c
adb=cbddad
aab=dbcdaa
bb=ddad
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 3097 | ⟨a, b | aabbaaaaabb=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 3283 | ⟨a, b | abbaabbbbba=1⟩ | φ(a) = b, φ(b) = a |