#2966 ⟨a, b | aaabbaabbba=1⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 11
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = b2a2ca3
- b-1 = b2d
- c-1 = d
- d-1 = c
- Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(b) = 0, c < d < b; deg(a) = 1
- Auxiliary generators:
- bbb=c
- aaaabbaa=d
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaabbaabbba=1 reversed:cdb/a bbb=c,aaaabbaa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbb=c
abbaac=bbaaca
aacad=bdabbaa
abbaabc=bbaacab
aacabd=bdabbaab
abbaabbc=bbaacabb
aacabbd=bdabbaabb
aacaad=bdaabbaa
aacaab=baaaac
aabbaab=caaaa
aaaabb=bbdaacaa
aacaaad=bdaaabbaa
aacaaab=bdacaaaac
aacaaaa=bd
aaaabaac=daabcaacaa
aaaabcaac=bbdaabbcaacaa
aaaabaab=daabbcaaaa
aaaabcaab=bbdaaccaaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 3112 | ⟨a, b | aabbaabbbaa=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 3136 | ⟨a, b | aabbbaaaabb=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 3155 | ⟨a, b | aabbbbaabba=1⟩ | φ(a) = b, φ(b) = a |
| 11 | 3276 | ⟨a, b | abbaaabbbba=1⟩ | φ(a) = b, φ(b) = a |