#3347 ⟨a, b, c | ab=aa, caa=c⟩
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 c is not injective:
-
c ⋅ a2 = c and c ⋅ 1 = c, however a2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b < c
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:ab=aa,caa=c abc - -
ab=aa
cb=ca
caa=c
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 3350 | ⟨a, b, c | ab=aa, cab=c⟩ | φ(a) = a, φ(b) = b, φ(c) = c |
| 8 | 3356 | ⟨a, b, c | ab=aa, cba=c⟩ | φ(a) = a, φ(b) = b, φ(c) = c |