#333 ⟨a, b | ababbaba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 8
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = ad2
- b-1 = abdc
- c-1 = d2
- d-1 = dc
- Reduced group presentation: ⟨a, b | aabaab-1⟩
- Isomorphism: φ(a) = b-1a, φ(b) = b
- Auxiliary generators:
- c = aa
- d = bab
- Reduction order:
- Left-to-right recursive path with deg(d) = deg(c) = 0, d < c; deg(a) = deg(b) = 1, a < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:ababbaba=1 dc/ab aa=c,bab=d morph:2/0,3/0
cd=dc
ddc=1
ca=ac
dda=add
aa=c
ba=dabdc
bda=adb
bdcb=add
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 6 | 83 | ⟨a, b | aabaa=b⟩ | Infinite cancellative non-commutative monoid | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 337 | ⟨a, b | abbabaab=1⟩ | φ(a) = bba, φ(b) = abdc |