#3187 ⟨a, b | ab=a, bba=aaa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a3 ⋅ a = a2 and a ⋅ a = a2, however a3 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,bba=aaa ab - -
ab=a
bba=aaa
aaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
14 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 9270 | ⟨a, b | ab=a, aaab=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9278 | ⟨a, b | ab=a, aaba=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9294 | ⟨a, b | ab=a, abaa=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9360 | ⟨a, b | ab=a, bbab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25434 | ⟨a, b | ab=a, aaabb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25450 | ⟨a, b | ab=a, aabab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25458 | ⟨a, b | ab=a, aabba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25482 | ⟨a, b | ab=a, abaab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25490 | ⟨a, b | ab=a, ababa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25506 | ⟨a, b | ab=a, abbaa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25620 | ⟨a, b | ab=a, bbabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25871 | ⟨a, b | ab=a, bbab=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25872 | ⟨a, b | ab=a, bbab=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25874 | ⟨a, b | ab=a, bbab=abaa⟩ | φ(a) = a, φ(b) = b |