#19530 ⟨a, b | aab=b, aabba=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ba = ba and b ⋅ a = ba, however ba ≠ a
- Not right cancellative, because right multiplication by b is not injective:
-
a2 ⋅ b = b and 1 ⋅ b = b, however a2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,aabba=ba ab - -
aab=b
bba=ba
bbb=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19578 | ⟨a, b | aab=b, baaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20070 | ⟨a, b | aab=b, aaba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20098 | ⟨a, b | aab=b, abba=aba⟩ | φ(a) = a, φ(b) = b |