#1671 ⟨a, b | aba=ab, 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:aba=ab,bab=b ab - -
ba=b
bb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
14 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 1673 | ⟨a, b | aba=ab, bba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5261 | ⟨a, b | aba=ab, baab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5263 | ⟨a, b | aba=ab, baba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5267 | ⟨a, b | aba=ab, bbaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12573 | ⟨a, b | abba=ab, baab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12575 | ⟨a, b | abba=ab, baba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12577 | ⟨a, b | abba=ab, babb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12579 | ⟨a, b | abba=ab, bbaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12581 | ⟨a, b | abba=ab, bbab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12583 | ⟨a, b | abba=ab, bbba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15876 | ⟨a, b | aba=ab, baaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15878 | ⟨a, b | aba=ab, baaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15882 | ⟨a, b | aba=ab, babaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15890 | ⟨a, b | aba=ab, bbaaa=b⟩ | φ(a) = a, φ(b) = b |