#598 ⟨a, b | aab=b, bba=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 ⋅ a2 = a and a ⋅ 1 = a, however a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, 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,bba=a ab - -
aaa=a
aab=b
bba=a
bbb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6394 | ⟨a, b | aab=b, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6406 | ⟨a, b | aab=b, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6418 | ⟨a, b | aab=b, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6430 | ⟨a, b | aab=b, bbaaa=a⟩ | φ(a) = a, φ(b) = b |