#5338 ⟨a, b | aaa=bb, aab=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 ⋅ ab = a2 and a ⋅ a = a2, however ab ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
ba ⋅ a = a2 and a ⋅ a = a2, however ba ≠ 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:aaa=bb,aab=aa a/b - -
aaaaa=aa
baa=aa
aab=aa
bb=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16088 | ⟨a, b | aab=aa, aaab=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 16092 | ⟨a, b | aab=aa, aaba=bb⟩ | φ(a) = a, φ(b) = b |