#9733 ⟨a, b | aa=1, abababb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ab2 has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ (ab)3 = b and b ⋅ 1 = b, however (ab)3 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
(ba)3 ⋅ b = b and 1 ⋅ b = b, however (ba)3 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,abababb=b ab - -
aa=1
bababb=ab
bababab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 10044 | ⟨a, b | aa=1, bababb=ab⟩ | φ(a) = a, φ(b) = b |