#10279 ⟨a, b | aa=1, ababb=bab⟩
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 b is not injective:
-
b ⋅ b3ab = b2ab and b ⋅ bab = b2ab, however b3ab ≠ bab
- Not right cancellative, because right multiplication by b is not injective:
-
bab ⋅ b = (ab)2 and aba ⋅ b = (ab)2, however bab ≠ aba
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,ababb=bab ab - -
aa=1
babb=abab
bbabab=abbbab
bbbbab=bbab
bababab=abbab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 10517 | ⟨a, b | aa=1, babb=abab⟩ | φ(a) = a, φ(b) = b |