#5321 ⟨a, b | aaa=ab, abb=ba⟩
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:
-
b ⋅ a = a5 and a4 ⋅ a = a5, however b ≠ a4
- 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,abb=ba a/b - -
aaaaaa=aaaa
ba=aaaaa
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15987 | ⟨a, b | aaa=ab, aaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 15991 | ⟨a, b | aaa=ab, aaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 15999 | ⟨a, b | aaa=ab, abaa=ba⟩ | φ(a) = a, φ(b) = b |