#5332 ⟨a, b | aaa=ab, bba=ab⟩
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 a is not injective:
-
a ⋅ b = a3 and a ⋅ a2 = a3, however b ≠ a2
- Not right cancellative, because right multiplication by a is not injective:
-
b2 ⋅ a = a3 and a2 ⋅ a = a3, however b2 ≠ a2
- 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,bba=ab a/b - -
aaaaaa=aaaa
ab=aaa
bba=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16483 | ⟨a, b | aaa=ab, bba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 16516 | ⟨a, b | aab=ba, bbb=aab⟩ | φ(a) = b, φ(b) = a |