#19240 ⟨a, b | aaa=a, aaaba=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element c 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 a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, however a2 ≠ 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:aaa=a,aaaba=ab acb ab=c morph:2/1
ab=c
ca=c
cb=cc
aaa=a
aac=c
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19784 | ⟨a, b | aaa=a, aaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19791 | ⟨a, b | aaa=a, aaba=aab⟩ | φ(a) = a, φ(b) = b |