#5237 ⟨a, b | aba=aa, baab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element bab has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ a2b = b and b ⋅ 1 = b, however a2b ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba2 ⋅ b = b and 1 ⋅ b = b, however ba2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=aa,baab=b ab - -
aba=aa
aaaa=aa
aaab=ab
baaa=ba
baab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15834 | ⟨a, b | aba=aa, babab=b⟩ | φ(a) = a, φ(b) = b |