#9262 ⟨a, b | ab=a, aaaa=bba⟩
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 = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a4 ⋅ a = a2 and a ⋅ a = a2, however a4 ≠ a
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,aaaa=bba a/b - -
aaaaa=aa
ab=a
bba=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 25418 | ⟨a, b | ab=a, aaaab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25426 | ⟨a, b | ab=a, aaaba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25442 | ⟨a, b | ab=a, aabaa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25474 | ⟨a, b | ab=a, abaaa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25870 | ⟨a, b | ab=a, bbab=aaaa⟩ | φ(a) = a, φ(b) = b |