#5329 ⟨a, b | aaa=ab, bab=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ a3 = ba and b ⋅ a = ba, however a3 ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
ba2 ⋅ a = ba and b ⋅ a = ba, however ba2 ≠ b
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaa=ab,bab=ba a/b - -
aaaaaa=aaaa
baaa=ba
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16015 | ⟨a, b | aaa=ab, baaa=ba⟩ | φ(a) = a, φ(b) = b |