#12236 ⟨a, b | aaab=aa, bbab=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a4 = a2 and a ⋅ a = a2, however a4 ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
a4 ⋅ a = a2 and a ⋅ a = a2, however a4 ≠ 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:aaab=aa,bbab=a a/b - -
aaaaa=aa
aab=aaaa
bbaa=abaaa
abab=abaaa
bbab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12346 | ⟨a, b | aaba=aa, bbab=a⟩ | φ(a) = a, φ(b) = b |