#4150 ⟨a, b | abb=aaa, baa=a⟩
Contents
- Properties
- Rewriting system
- Anti-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 ⋅ a4 = a and a ⋅ 1 = a, however a4 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a4 ⋅ a = a and 1 ⋅ a = a, however a4 ≠ 1
- 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:abb=aaa,baa=a a/b - -
aaaaa=a
ba=aaaa
abb=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6372 | ⟨a, b | aab=a, bbabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6650 | ⟨a, b | aab=a, bbab=aa⟩ | φ(a) = a, φ(b) = b |