#973 ⟨a, b, c | ab=a, bca=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b ⋅ b = b and 1 ⋅ b = b, however b ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b < c
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:ab=a,bca=b abc - -
ab=a
bb=b
aca=a
bca=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 5369 | ⟨a, b, c | ab=a, bbca=b⟩ | φ(a) = a, φ(b) = b, φ(c) = c |
| 8 | 5381 | ⟨a, b, c | ab=a, bcab=b⟩ | φ(a) = a, φ(b) = b, φ(c) = c |