#10004 ⟨a, b | aa=1, ababba=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 ⋅ ab2 = b2 and b ⋅ b = b2, however ab2 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
bab ⋅ b = b2 and b ⋅ b = b2, however bab ≠ b
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,ababba=bb ab - -
aa=1
bba=abb
bbb=abb
babb=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 10280 | ⟨a, b | aa=1, ababb=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 10288 | ⟨a, b | aa=1, abbab=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 10518 | ⟨a, b | aa=1, babb=abba⟩ | φ(a) = a, φ(b) = b |