#1609 ⟨a, b | aaa=bb, bbb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a2b has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ a3 = b and b ⋅ 1 = b, however a3 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
a3 ⋅ b = b and 1 ⋅ b = b, however a3 ≠ 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:aaa=bb,bbb=b a/b - -
aaaaaa=aaa
baaa=b
aaab=b
bb=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5077 | ⟨a, b | aaa=bb, aaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19781 | ⟨a, b | aaa=a, aaaa=bbb⟩ | φ(a) = b, φ(b) = a |