#7141 ⟨a, b | bb=aa, aaab=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ab has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a5 = a2 and a ⋅ a = a2, however a5 ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
a5 ⋅ a = a2 and a ⋅ a = a2, however a5 ≠ a
- 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:bb=aa,aaab=aa a/b - -
aaaaaa=aa
baa=aaaaa
aab=aaaaa
bb=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7144 | ⟨a, b | bb=aa, aaab=bb⟩ | φ(a) = a, φ(b) = b |
| 10 | 7145 | ⟨a, b | bb=aa, aaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7148 | ⟨a, b | bb=aa, aaba=bb⟩ | φ(a) = a, φ(b) = b |