#19546 ⟨a, b | aab=b, ababa=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ba = ba and b ⋅ a = ba, however ba ≠ a
- Not right cancellative, because right multiplication by b is not injective:
-
a2 ⋅ b = b and 1 ⋅ b = b, 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,ababa=ba ab - -
aab=b
bba=ba
bbb=bb
baba=aba
babb=abb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20130 | ⟨a, b | aab=b, baba=aba⟩ | φ(a) = a, φ(b) = b |