#7816 ⟨a, b | aaa=1, babbb=ba⟩
Contents
- Properties
- Rewriting system
- Anti-isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element aba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b3 = b and b ⋅ 1 = b, however b3 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b3 ⋅ b = b and 1 ⋅ b = b, however b3 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=1,babbb=ba ab - -
aaa=1
bbbb=b
babbb=ba
baabbb=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21703 | ⟨a, b | aaa=1, aabbbab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 21743 | ⟨a, b | aaa=1, abbbaab=b⟩ | φ(a) = a, φ(b) = b |