#1370 ⟨a, b | aaabbaabba=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 = a3d
- b-1 = a2b2cb
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aaaabbaabb⟩
- Isomorphism: φ(a) = a, φ(b) = b
- Auxiliary generators:
- c = aaaa
- d = bbaabb
- Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(d) = 1; deg(a) = deg(b) = 2, a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaabbaabba=1 c/d/ab aaaa=c,bbaabb=d magic:0
dc=1
cd=1
ca=ac
da=ad
cccb=bccc
db=ccbddd
cbb=bbc
baa=aacbd
aaaa=c
bbbb=aadd
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 10 | 2077 | ⟨a, b | abbaabba=bb⟩ | 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 | 1439 | ⟨a, b | aabbaaaabb=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1444 | ⟨a, b | aabbaabbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1528 | ⟨a, b | abbaaaabba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1534 | ⟨a, b | abbaabbbba=1⟩ | φ(a) = b, φ(b) = a |