#7197 ⟨a, b | bb=aa, aab=aaa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ab = a3 and a ⋅ a2 = a3, however ab ≠ a2
- Not right cancellative, because right multiplication by a is not injective:
-
ba ⋅ a = a3 and a2 ⋅ a = a3, however ba ≠ a2
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:bb=aa,aab=aaa ab - -
bb=aa
aab=aaa
baa=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7201 | ⟨a, b | bb=aa, abb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7204 | ⟨a, b | bb=aa, baa=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 7207 | ⟨a, b | bb=aa, bbb=aaa⟩ | φ(a) = a, φ(b) = b |