#5374 ⟨a, b | aab=ab, aba=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by c is not injective:
-
c ⋅ a = c and c ⋅ 1 = c, however a ≠ 1
- Not right cancellative, because right multiplication by c is not injective:
-
a ⋅ c = c and 1 ⋅ c = c, however a ≠ 1
- Auxiliary generators:
- c = ab
- Reduction order:
- Left-to-right shortlex with a < c < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aab=ab,aba=ab acb ab=c morph:2/1
ac=c
ab=c
ca=c
cb=cc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16154 | ⟨a, b | aab=ab, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16382 | ⟨a, b | aba=ab, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16499 | ⟨a, b | aab=ab, aba=aab⟩ | φ(a) = a, φ(b) = b |