#21787 ⟨a, b | aaa=1, bbabbbb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element ba2 has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ab5 = b and b ⋅ 1 = b, however ab5 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
bab4 ⋅ b = b and 1 ⋅ b = b, however bab4 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=1,bbabbbb=b ab - -
aaa=1
bbab=babb
babbbbb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 21789 | ⟨a, b | aaa=1, bbbabbb=b⟩ | φ(a) = a, φ(b) = b |