#3065 ⟨a, b, c | abc=a, cab=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ bc = a and a ⋅ 1 = a, however bc ≠ 1
- Reduction order:
- Left-to-right shortlex with b < c < a
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:abc=a,cab=a bca - -
ac=ca
cab=a
abc=a
aab=aba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 3419 | ⟨a, b, c | ba=ab, abc=a⟩ | φ(a) = ab, φ(b) = c, φ(c) = b |
| 8 | 3420 | ⟨a, b, c | ba=ab, abc=b⟩ | φ(a) = c, φ(b) = ab, φ(c) = b |