#2936 ⟨a, b | ab=a, aaaaa=a⟩
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:
-
a4 ⋅ a = a and 1 ⋅ a = a, however a4 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,aaaaa=a ab - -
ab=a
aaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
28 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8714 | ⟨a, b | ab=a, aaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8716 | ⟨a, b | ab=a, aaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8720 | ⟨a, b | ab=a, aaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8728 | ⟨a, b | ab=a, aabaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8744 | ⟨a, b | ab=a, abaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8985 | ⟨a, b | ab=a, aaaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 15545 | ⟨a, b | aab=aa, aaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24338 | ⟨a, b | ab=a, aaaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24342 | ⟨a, b | ab=a, aaaabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24344 | ⟨a, b | ab=a, aaaabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24350 | ⟨a, b | ab=a, aaabaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24352 | ⟨a, b | ab=a, aaababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24356 | ⟨a, b | ab=a, aaabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24366 | ⟨a, b | ab=a, aabaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24368 | ⟨a, b | ab=a, aabaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24372 | ⟨a, b | ab=a, aababaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24380 | ⟨a, b | ab=a, aabbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24398 | ⟨a, b | ab=a, abaaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24400 | ⟨a, b | ab=a, abaaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24404 | ⟨a, b | ab=a, abaabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24412 | ⟨a, b | ab=a, ababaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24428 | ⟨a, b | ab=a, abbaaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24865 | ⟨a, b | ab=a, aaaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24869 | ⟨a, b | ab=a, aaaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24877 | ⟨a, b | ab=a, aaabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24893 | ⟨a, b | ab=a, aabaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24925 | ⟨a, b | ab=a, abaaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25407 | ⟨a, b | ab=a, aaaaa=abb⟩ | φ(a) = a, φ(b) = b |