#1641 ⟨a, b | aab=ba, bab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ a = b and b ⋅ 1 = b, however a ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b ⋅ b = b and 1 ⋅ b = b, however b ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ba,bab=b ab - -
ba=b
bb=b
aab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
15 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 1643 | ⟨a, b | aab=ba, bba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5165 | ⟨a, b | aab=ba, aabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5177 | ⟨a, b | aab=ba, baab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5179 | ⟨a, b | aab=ba, baba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5183 | ⟨a, b | aab=ba, bbaa=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5249 | ⟨a, b | aba=ab, aabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12480 | ⟨a, b | aabb=ba, babb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15684 | ⟨a, b | aab=ba, aabab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15686 | ⟨a, b | aab=ba, aabba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15708 | ⟨a, b | aab=ba, baaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15710 | ⟨a, b | aab=ba, baaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15714 | ⟨a, b | aab=ba, babaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15722 | ⟨a, b | aab=ba, bbaaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15852 | ⟨a, b | aba=ab, aabab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15854 | ⟨a, b | aba=ab, aabba=b⟩ | φ(a) = a, φ(b) = b |