#7158 ⟨a, b | ab=aa, aab=aaa⟩
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 ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
| # | Rule | Proof |
|---|
| 1. |
ab ⇒ a2 |
[1] |
# ab:ab=aa,aab=aaa ab - -
ab=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7159 | ⟨a, b | ab=aa, aba=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7160 | ⟨a, b | ab=aa, aba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7161 | ⟨a, b | ab=aa, abb=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7162 | ⟨a, b | ab=aa, abb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7163 | ⟨a, b | ab=aa, abb=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7172 | ⟨a, b | ab=aa, bab=baa⟩ | φ(a) = a, φ(b) = b |