#10008 ⟨a, b | aa=1, ababbb=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ abab2 = b2 and b ⋅ b = b2, however abab2 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
b(ab)2 ⋅ b = b2 and b ⋅ b = b2, however b(ab)2 ≠ b
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,ababbb=bb ab - -
aa=1
babbb=abb
bababb=bb
babbabb=ababb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 10327 | ⟨a, b | aa=1, babbb=abb⟩ | φ(a) = a, φ(b) = b |