#890 ⟨a, b | aa=a, abba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,abba=a ab - -
aa=a
abba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
17 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2868 | ⟨a, b | aa=a, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 9 | 3019 | ⟨a, b | aa=a, abba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 5138 | ⟨a, b | aab=ab, abba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8580 | ⟨a, b | aa=a, aaabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8590 | ⟨a, b | aa=a, aabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8862 | ⟨a, b | aa=a, aabba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9150 | ⟨a, b | aa=a, abba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 14805 | ⟨a, b | abba=a, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15413 | ⟨a, b | aaa=aa, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15621 | ⟨a, b | aab=ab, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 15633 | ⟨a, b | aab=ab, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24056 | ⟨a, b | aa=a, aaaabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24068 | ⟨a, b | aa=a, aaabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24611 | ⟨a, b | aa=a, aaabba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24631 | ⟨a, b | aa=a, aabbaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25160 | ⟨a, b | aa=a, aabba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25674 | ⟨a, b | aa=a, abba=aaaa⟩ | φ(a) = a, φ(b) = b |