#10287 ⟨a, b | aa=1, abbab=bab⟩
Contents
- Properties
- Rewriting system
- Anti-isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ (ab)2 = bab and b ⋅ ab = bab, however (ab)2 ≠ ab
- Not right cancellative, because right multiplication by b is not injective:
-
(ba)2 ⋅ b = bab and ba ⋅ b = bab, however (ba)2 ≠ ba
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,abbab=bab ab - -
aa=1
bbab=abab
babab=bab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 10522 | ⟨a, b | aa=1, babb=baba⟩ | φ(a) = a, φ(b) = b |