#27639 ⟨a, b | aa=1, ababab=bab⟩
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 b is not injective:
-
b ⋅ bab = bab and b ⋅ ab = bab, however bab ≠ ab
- Not right cancellative, because right multiplication by b is not injective:
-
b2a ⋅ b = bab and ba ⋅ b = bab, however b2a ≠ ba
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,ababab=bab ab - -
aa=1
bbab=bab
babab=abab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 28254 | ⟨a, b | aa=1, babab=abab⟩ | φ(a) = a, φ(b) = b |