#8614 ⟨a, b | aa=a, abbbab=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 ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,abbbab=a ab - -
aa=a
aba=ab
abba=abb
abbba=abbb
abbbb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15871 | ⟨a, b | aba=ab, abbbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24098 | ⟨a, b | aa=a, aabbbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24122 | ⟨a, b | aa=a, ababbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24132 | ⟨a, b | aa=a, abbabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24138 | ⟨a, b | aa=a, abbbaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24677 | ⟨a, b | aa=a, abbbab=aa⟩ | φ(a) = a, φ(b) = b |