#6324 ⟨a, b | aab=a, aaabb=a⟩
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 ⋅ ab = a and a ⋅ 1 = a, however ab ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
| # | Rule | Proof |
|---|
| 1. |
a2b ⇒ a |
[1] |
# ab:aab=a,aaabb=a ab - -
aab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6328 | ⟨a, b | aab=a, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6602 | ⟨a, b | aab=a, aaab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6606 | ⟨a, b | aab=a, aaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6611 | ⟨a, b | aab=a, aabb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6636 | ⟨a, b | aab=a, baab=ba⟩ | φ(a) = a, φ(b) = b |