#7037 ⟨a, b | bb=aa, aaaab=b⟩
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 b is not injective:
-
a4 ⋅ b = b and 1 ⋅ b = b, however a4 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:bb=aa,aaaab=b ab - -
bb=aa
baa=aab
aaaab=b
aaaaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7043 | ⟨a, b | bb=aa, aabaa=b⟩ | φ(a) = a, φ(b) = b |