#4180 ⟨a, b | baa=abb, bba=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b4 = ab2 and a ⋅ b2 = ab2, however b4 ≠ b2
- Not right cancellative, because right multiplication by a is not injective:
-
b2 ⋅ a = a and 1 ⋅ a = a, however b2 ≠ 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:baa=abb,bba=a b/a - -
abbbb=abb
bba=a
aa=babb
ababb=abb
ababa=aba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6681 | ⟨a, b | aab=b, abaa=bb⟩ | φ(a) = b, φ(b) = a |