#21032 ⟨a, b | ab=aa, bbba=aaa⟩
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:
-
b3 ⋅ a = a3 and a2 ⋅ a = a3, however b3 ≠ a2
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,bbba=aaa ab - -
ab=aa
bbba=aaa
aaaaa=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21033 | ⟨a, b | ab=aa, bbba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 21034 | ⟨a, b | ab=aa, bbba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 21035 | ⟨a, b | ab=aa, bbba=abb⟩ | φ(a) = a, φ(b) = b |