#4175 ⟨a, b | baa=aab, bba=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 left cancellative, because left multiplication by b is not injective:
-
b ⋅ ba = b and b ⋅ 1 = b, however ba ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 1
- Reduction order:
- Left-to-right shortlex with b < a
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:baa=aab,bba=b ba - -
bba=b
bab=b
aab=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6366 | ⟨a, b | aab=a, bbaaa=a⟩ | φ(a) = b, φ(b) = a |
| 10 | 6647 | ⟨a, b | aab=a, bbaa=ab⟩ | φ(a) = b, φ(b) = a |