#93 ⟨a, b | aa=1, bab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 6
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ab = b and b ⋅ 1 = b, however ab ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,bab=b ab - -
aa=1
bab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
19 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 1107 | ⟨a, b | aa=1, aabab=b⟩ | φ(a) = a, φ(b) = b |
| 8 | 1125 | ⟨a, b | aa=1, baaab=b⟩ | φ(a) = a, φ(b) = b |
| 8 | 1184 | ⟨a, b | aa=1, abab=ab⟩ | φ(a) = a, φ(b) = b |
| 8 | 1249 | ⟨a, b | aa=1, bab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9667 | ⟨a, b | aa=1, aaaabab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9689 | ⟨a, b | aa=1, aabaaab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9695 | ⟨a, b | aa=1, aababaa=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9761 | ⟨a, b | aa=1, baaaaab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9948 | ⟨a, b | aa=1, aaabab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9965 | ⟨a, b | aa=1, aababa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9987 | ⟨a, b | aa=1, abaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10211 | ⟨a, b | aa=1, aaaab=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10234 | ⟨a, b | aa=1, aabaa=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10237 | ⟨a, b | aa=1, aabab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10240 | ⟨a, b | aa=1, aabab=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 10270 | ⟨a, b | aa=1, ababa=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 10305 | ⟨a, b | aa=1, baaab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10482 | ⟨a, b | aa=1, abab=aaab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10485 | ⟨a, b | aa=1, abab=abaa⟩ | φ(a) = a, φ(b) = b |