#1305 ⟨a, b | aaaaabbbba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = a5d
- b-1 = b3c
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aaaaaabbbb⟩
- Isomorphism: φ(a) = a, φ(b) = b
- Auxiliary generators:
- c = aaaaaa
- d = bbbb
- Reduction order:
- Left-to-right shortlex with a < b < c < d
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaaaabbbba=1 abcd aaaaaa=c,bbbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbbb=d
aaaaaa=c
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 10 | 2372 | ⟨a, b | aaaaaa=bbbb⟩ | Infinite cancellative non-commutative monoid | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1334 | ⟨a, b | aaaabbbbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1384 | ⟨a, b | aaabbbbaaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1390 | ⟨a, b | aaabbbbbba=1⟩ | φ(a) = b, φ(b) = a |
| 10 | 1472 | ⟨a, b | aabbbbbbaa=1⟩ | φ(a) = b, φ(b) = a |