#20520 ⟨a, b | ab=aa, aaaaaa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- 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:
-
a5 ⋅ a = a and 1 ⋅ a = a, however a5 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaaaa=a ab - -
ab=aa
aaaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
31 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20522 | ⟨a, b | ab=aa, aaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20524 | ⟨a, b | ab=aa, aaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20526 | ⟨a, b | ab=aa, aaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20528 | ⟨a, b | ab=aa, aaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20530 | ⟨a, b | ab=aa, aaabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20532 | ⟨a, b | ab=aa, aaabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20534 | ⟨a, b | ab=aa, aaabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20536 | ⟨a, b | ab=aa, aabaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20538 | ⟨a, b | ab=aa, aabaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20540 | ⟨a, b | ab=aa, aababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20542 | ⟨a, b | ab=aa, aababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20544 | ⟨a, b | ab=aa, aabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20546 | ⟨a, b | ab=aa, aabbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20548 | ⟨a, b | ab=aa, aabbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20550 | ⟨a, b | ab=aa, aabbbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20552 | ⟨a, b | ab=aa, abaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20554 | ⟨a, b | ab=aa, abaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20556 | ⟨a, b | ab=aa, abaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20558 | ⟨a, b | ab=aa, abaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20560 | ⟨a, b | ab=aa, ababaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20562 | ⟨a, b | ab=aa, ababab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20564 | ⟨a, b | ab=aa, ababba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20566 | ⟨a, b | ab=aa, ababbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20568 | ⟨a, b | ab=aa, abbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20570 | ⟨a, b | ab=aa, abbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20572 | ⟨a, b | ab=aa, abbaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20574 | ⟨a, b | ab=aa, abbabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20576 | ⟨a, b | ab=aa, abbbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20578 | ⟨a, b | ab=aa, abbbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20580 | ⟨a, b | ab=aa, abbbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20582 | ⟨a, b | ab=aa, abbbbb=a⟩ | φ(a) = a, φ(b) = b |