#960 ⟨a, b | aa=a, aba=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Auxiliary generators:
- c = ab
- Reduction order:
- Left-to-right shortlex with a < c < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aa=a,aba=ab acb ab=c morph:2/1
aa=a
ac=c
ab=c
ca=c
cb=cc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
13 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3008 | ⟨a, b | aa=a, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3138 | ⟨a, b | aa=a, aba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 8848 | ⟨a, b | aa=a, aaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 8856 | ⟨a, b | aa=a, aabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9120 | ⟨a, b | aa=a, aaab=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9127 | ⟨a, b | aa=a, aaba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24596 | ⟨a, b | aa=a, aaaaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24604 | ⟨a, b | aa=a, aaabaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25124 | ⟨a, b | aa=a, aaaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25131 | ⟨a, b | aa=a, aaaba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25147 | ⟨a, b | aa=a, aabaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25662 | ⟨a, b | aa=a, aaba=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25666 | ⟨a, b | aa=a, abaa=aaab⟩ | φ(a) = a, φ(b) = b |