#16165 ⟨a, b | aab=ab, abab=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a2 = a2 and a ⋅ a = a2, however a2 ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a2 and a ⋅ a = a2, however a2 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ab,abab=aa ab - -
aaa=aa
aab=ab
aba=ab
abb=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16393 | ⟨a, b | aba=ab, abab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 16397 | ⟨a, b | aba=ab, abba=aa⟩ | φ(a) = a, φ(b) = b |