#19550 ⟨a, b | aab=b, ababb=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b5 = b2 and b ⋅ b = b2, however b5 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
a2 ⋅ b = b and 1 ⋅ b = b, however a2 ≠ 1
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,ababb=ba b/a - -
bbbbbb=bb
babbbb=ba
bbbba=abbbb
aab=b
aba=babb
abba=bbbab
abbba=bbabbb
baa=bbbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20138 | ⟨a, b | aab=b, babb=aba⟩ | φ(a) = a, φ(b) = b |