#377 ⟨a, b | aababaa=a⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 8
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ (ab)2a2 = a and a ⋅ 1 = a, however (ab)2a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2(ba)2 ⋅ a = a and 1 ⋅ a = a, however a2(ba)2 ≠ 1
- Enveloping group: ⟨a, b | aabb⟩
- Auxiliary generators:
- c = aa
- Reduction order:
- Left-to-right shortlex with a < c < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aababaa=a acb aa=c morph:2/0
aa=c
ca=ac
abac=acba
abcc=acbc
cbac=ccba
cbcc=ccbc
cbaba=ababc
cbabc=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 395 | ⟨a, b | abaaaba=a⟩ | φ(a) = a, φ(b) = b |