#5419 ⟨a, b | aba=ab, bab=ab⟩
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 ⋅ ba = ab and a ⋅ b = ab, however ba ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
ba ⋅ b = ab and a ⋅ b = ab, however ba ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=ab,bab=ab ab - -
aba=ab
abb=aab
bab=ab
aaab=aab
baab=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16414 | ⟨a, b | aba=ab, baba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16539 | ⟨a, b | aba=ab, bab=aba⟩ | φ(a) = a, φ(b) = b |