#4711 ⟨a, b | aaba=a, babb=b⟩
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 a is not injective:
-
a ⋅ ba2 = a and a ⋅ 1 = a, however ba2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
aba ⋅ a = a and 1 ⋅ a = a, however aba ≠ 1
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaba=a,babb=b a/b - -
abaa=a
aaba=a
bba=baa
baab=b
baaab=bb
abb=aab
bbb=baaaab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 4748 | ⟨a, b | abba=a, baab=b⟩ | φ(a) = a, φ(b) = b |