#21020 ⟨a, b | ab=aa, bbaa=baa⟩
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 ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
b2a ⋅ a = ba2 and ba ⋅ a = ba2, however b2a ≠ ba
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,bbaa=baa ab - -
ab=aa
bbaa=baa
aaaaa=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21021 | ⟨a, b | ab=aa, bbaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21028 | ⟨a, b | ab=aa, bbab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 21029 | ⟨a, b | ab=aa, bbab=bab⟩ | φ(a) = a, φ(b) = b |