#6342 ⟨a, b | aab=a, abbaa=a⟩
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 a is not injective:
-
a ⋅ ac = a and a ⋅ 1 = a, however ac ≠ 1
- Not right cancellative, because right multiplication by c is not injective:
-
ac ⋅ c = c and 1 ⋅ c = c, however ac ≠ 1
- Auxiliary generators:
- c = abb
- 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=a,abbaa=a acb abb=c morph:3/1
ab=ac
ca=ac
cb=cc
aac=a
acc=c
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6623 | ⟨a, b | aab=a, abba=ab⟩ | φ(a) = a, φ(b) = b |