#7102 ⟨a, b | ab=aa, bbaa=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
b2a ⋅ a = a2 and a ⋅ a = a2, however b2a ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,bbaa=aa ab - -
ab=aa
bbaa=aa
aaaaa=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7103 | ⟨a, b | ab=aa, bbaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7106 | ⟨a, b | ab=aa, bbab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7107 | ⟨a, b | ab=aa, bbab=ab⟩ | φ(a) = a, φ(b) = b |