#6385 ⟨a, b | aab=b, aaaab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- 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 a < b
- Certificate: derivations of all rewriting rules from the defining relations.
| # | Rule | Proof |
|---|
| 1. |
a2b ⇒ b |
[1] |
# ab:aab=b,aaaab=b ab - -
aab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6667 | ⟨a, b | aab=b, aaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6672 | ⟨a, b | aab=b, aaba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6677 | ⟨a, b | aab=b, aabb=bb⟩ | φ(a) = a, φ(b) = b |
| 10 | 6701 | ⟨a, b | aab=b, baab=bb⟩ | φ(a) = a, φ(b) = b |