#6787 ⟨a, b | aba=b, abbb=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b3 = b2 and b ⋅ b = b2, however b3 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
b3 ⋅ b = b2 and b ⋅ b = b2, however b3 ≠ b
- Reduction order:
- Left-to-right shortlex with b < a
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=b,abbb=bb ba - -
bba=bbb
abb=bbb
aba=b
bbbb=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6794 | ⟨a, b | aba=b, babb=bb⟩ | φ(a) = a, φ(b) = b |