#4684 ⟨a, b | aaab=b, abba=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not right cancellative, because right multiplication by b is not injective:
-
a3 ⋅ b = b and 1 ⋅ b = b, however a3 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaab=b,abba=b ab - -
baa=abb
bba=aab
aaab=b
babb=aaba
bbbbb=ababa
bababa=ababab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 13077 | ⟨a, b | baa=abb, abba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 13078 | ⟨a, b | baa=abb, abbb=a⟩ | φ(a) = b, φ(b) = a |