#3501 ⟨a, b | aaabbabbaa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a(ab2)2a2 = a and a ⋅ 1 = a, however a(ab2)2a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a3(b2a)2 ⋅ a = a and 1 ⋅ a = a, however a3(b2a)2 ≠ 1
- Auxiliary generators:
- c = abba
- Reduction order:
- Left-to-right shortlex with b < a < c
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaabbabbaa=a bac abba=c morph:4/0
abba=c
cbba=abbc
caaa=aaac
caac=a
aabbc=abbca
acbbc=abbcc
cabbc=cbbca
ccbbc=cbbcc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 3799 | ⟨a, b | abbaaaabba=a⟩ | φ(a) = a, φ(b) = b |