#1693 ⟨a, b | aabababaa=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 c is not injective:
-
c ⋅ ba2c = c and c ⋅ 1 = c, however ba2c ≠ 1
- Not right cancellative, because right multiplication by c is not injective:
-
cba2 ⋅ c = c and 1 ⋅ c = c, however cba2 ≠ 1
- Auxiliary generators:
- c = ababa
- Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(b) = deg(a) = 1, b < a
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aabababaa=a c/ba ababa=c morph:5/0
ccbc=cbcc
ccba=cbca
abc=cba
acbc=cbac
caa=aac
cacac=a
cbaac=c
aba=cac
acba=cbaa
cbaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1757 | ⟨a, b | abaaababa=a⟩ | φ(a) = a, φ(b) = b |