#4666 ⟨a, b | aaab=a, baba=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a2b = a and a ⋅ 1 = a, 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:aaab=a,baba=b ab - -
aba=aab
bba=bab
aaab=a
baab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 4670 | ⟨a, b | aaab=a, bbaa=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 4709 | ⟨a, b | aaba=a, baba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 4713 | ⟨a, b | aaba=a, bbaa=b⟩ | φ(a) = a, φ(b) = b |