#12591 ⟨a, b | abba=ba, bbaa=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b = b and b ⋅ 1 = b, however b ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
a ⋅ b = b and 1 ⋅ b = b, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:abba=ba,bbaa=b ab - -
ab=b
bb=b
baa=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15634 | ⟨a, b | aab=ab, abbaa=b⟩ | φ(a) = a, φ(b) = b |