#15995 ⟨a, b | aaa=ab, aabb=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- 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:
-
b ⋅ a = a6 and a5 ⋅ a = a6, however b ≠ a5
- 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,aabb=ba a/b - -
aaaaaaa=aaaa
ba=aaaaaa
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16003 | ⟨a, b | aaa=ab, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 16007 | ⟨a, b | aaa=ab, abba=ba⟩ | φ(a) = a, φ(b) = b |