#2914 ⟨a, b | aaabaabaaba=1⟩
Quick links
- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 11
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = a3b3c
- b-1 = b2c2
- c-1 = b3c
- d-1 = c
- Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = deg(d) = 1, a < d
- Auxiliary generators:
- aaaa=c
- baabaab=d
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaabaabaaba=1 bc/ad aaaa=c,baabaab=d magic:0
cb=bc
bbbcc=1
ca=ac
bbba=abbb
d=bbbc
baa=aab
aaaa=c
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 3011 | ⟨a, b | aabaaaabaab=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 3029 | ⟨a, b | aabaabaaaab=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 3032 | ⟨a, b | aabaabaabaa=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 3178 | ⟨a, b | abaaaabaaba=1⟩ | φ(a) = a, φ(b) = b |