#591 ⟨a, b | aab=a, bba=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ab = a and a ⋅ 1 = a, however ab ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
ab ⋅ a = a and 1 ⋅ a = a, however ab ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=a,bba=b ab - -
aab=a
aba=a
bab=b
bba=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6363 | ⟨a, b | aab=a, babba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6369 | ⟨a, b | aab=a, bbaab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6371 | ⟨a, b | aab=a, bbaba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6375 | ⟨a, b | aab=a, bbbaa=b⟩ | φ(a) = a, φ(b) = b |