#6466 ⟨a, b | aba=a, ababb=a⟩
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 ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
ab ⋅ a = a and 1 ⋅ a = a, however ab ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=a,ababb=a ab - -
aba=a
abb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6757 | ⟨a, b | aba=a, babb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6827 | ⟨a, b | aba=a, abb=aba⟩ | φ(a) = a, φ(b) = b |