#590 ⟨a, b | aab=a, bba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a2 = a and a ⋅ 1 = a, however a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, however a2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=a,bba=a ab - -
ab=aa
aaa=a
bba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6368 | ⟨a, b | aab=a, bbaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6370 | ⟨a, b | aab=a, bbaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6395 | ⟨a, b | aab=b, aabba=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 6419 | ⟨a, b | aab=b, baaba=b⟩ | φ(a) = b, φ(b) = a |
| 10 | 6646 | ⟨a, b | aab=a, bbaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 6651 | ⟨a, b | aab=a, bbab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6687 | ⟨a, b | aab=b, abba=ab⟩ | φ(a) = b, φ(b) = a |
| 10 | 6814 | ⟨a, b | aab=a, bba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 6823 | ⟨a, b | aab=b, bba=aab⟩ | φ(a) = b, φ(b) = a |