#1610 ⟨a, b | aab=aa, aba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element ab2 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.
# ab:aab=aa,aba=a ab - -
aaa=aa
aab=aa
aba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19635 | ⟨a, b | aba=a, aaaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19650 | ⟨a, b | aba=a, aabab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19662 | ⟨a, b | aba=a, abaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20191 | ⟨a, b | aba=a, aaba=aab⟩ | φ(a) = a, φ(b) = b |