#1723 ⟨a, b | aabbabbaa=a⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ (ab2)2a2 = a and a ⋅ 1 = a, however (ab2)2a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2(b2a)2 ⋅ a = a and 1 ⋅ a = a, however a2(b2a)2 ≠ 1
- Enveloping group: ⟨a, b | aaabbabb⟩
- 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:aabbabbaa=a acb aa=c morph:2/0
aa=c
ca=ac
abbac=acbba
abbcc=acbbc
cbbac=ccbba
cbbcc=ccbbc
cbbabba=abbabbc
cbbabbc=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1801 | ⟨a, b | abbaaabba=a⟩ | φ(a) = a, φ(b) = b |