#4164 ⟨a, b | abb=aba, baa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b 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:abb=aba,baa=a ab - -
ba=aa
aaa=a
abb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6407 | ⟨a, b | aab=b, abbaa=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 6476 | ⟨a, b | aba=a, baabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6711 | ⟨a, b | aab=b, bbaa=ab⟩ | φ(a) = b, φ(b) = a |