#16197 ⟨a, b | aab=ab, bbab=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ba = ab and a ⋅ b = ab, however ba ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
b6a ⋅ b = ab and a ⋅ b = ab, however b6a ≠ a
- Reduction order:
- Right-to-left recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ab,bbab=aa reversed:b/a - -
bbbbbbab=ab
abb=bbbbab
aa=bbab
aba=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16425 | ⟨a, b | aba=ab, bbab=aa⟩ | φ(a) = a, φ(b) = b |