#5414 ⟨a, b | aab=bb, bba=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ab has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ aba = a2 and a ⋅ a = a2, however aba ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
a2b ⋅ a = a2 and a ⋅ a = a2, however a2b ≠ a
- 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:aab=bb,bba=aa a/b - -
aaaaaa=aaa
baa=aaaa
aaba=aa
bb=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16281 | ⟨a, b | aab=bb, aaba=aa⟩ | φ(a) = a, φ(b) = b |