#1908 ⟨a, b | aab=b, aaaaa=1⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- 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:aab=b,aaaaa=1 ab - -
ab=b
aaaaa=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 4414 | ⟨a, b | aaab=b, aaaaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4854 | ⟨a, b | aab=ab, aaaaa=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 11724 | ⟨a, b | aaab=ab, aaaaa=1⟩ | φ(a) = a, φ(b) = b |
| 11 | 11884 | ⟨a, b | aaba=ba, aaaaa=1⟩ | φ(a) = a, φ(b) = b |