#16068 ⟨a, b | aaa=bb, abbb=ab⟩
Contents
- Properties
- Rewriting system
- Anti-isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a2b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ba3 = ab and a ⋅ b = ab, however ba3 ≠ b
- Not right cancellative, because right multiplication by a is not injective:
-
a6 ⋅ a = a4 and a3 ⋅ a = a4, however a6 ≠ a3
- 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=bb,abbb=ab a/b - -
aaaaaaa=aaaa
baaaaaa=baaa
abaaa=ab
aaab=baaa
bb=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16076 | ⟨a, b | aaa=bb, babb=ba⟩ | φ(a) = a, φ(b) = b |