#18942 ⟨a, b | aab=a, bbabbb=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a5 = a and a ⋅ 1 = a, however a5 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a5 ⋅ a = a and 1 ⋅ a = a, however a5 ≠ 1
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=a,bbabbb=a a/b - -
aaaaaa=a
ab=aaaaa
bba=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19484 | ⟨a, b | aab=a, bbabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 19926 | ⟨a, b | aab=a, aaaa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20024 | ⟨a, b | aab=a, bbab=aaa⟩ | φ(a) = a, φ(b) = b |