#516 ⟨a, b | aab=a, abab=1⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- 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
- Not right cancellative, because right multiplication by bab is not injective:
-
(ba)2 ⋅ bab = bab and 1 ⋅ bab = bab, however (ba)2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=a,abab=1 ab - -
aab=a
abab=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 3835 | ⟨a, b | aaba=aa, abab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 3962 | ⟨a, b | abba=ab, baba=1⟩ | φ(a) = b, φ(b) = a |
| 10 | 6051 | ⟨a, b | aab=a, aabbab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 6057 | ⟨a, b | aab=a, abaabb=1⟩ | φ(a) = a, φ(b) = b |