#6464 ⟨a, b | aba=a, ababa=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 ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
ab ⋅ a = a and 1 ⋅ a = 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. |
aba ⇒ a |
[1] |
# ab:aba=a,ababa=a ab - -
aba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6733 | ⟨a, b | aba=a, aaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6742 | ⟨a, b | aba=a, abab=ab⟩ | φ(a) = a, φ(b) = b |