#19614 ⟨a, b | aab=b, bbabb=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 ⋅ ba2 = b2 and b ⋅ b = b2, however ba2 ≠ b
- 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 b < a
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,bbabb=ba ba - -
bab=bba
aab=b
bbbb=baa
bbaa=bb
baaa=ba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19622 | ⟨a, b | aab=b, bbbab=ba⟩ | φ(a) = a, φ(b) = b |