#1658 ⟨a, b, c | aab=ba, abc=1⟩
Contents
- Properties
- Rewriting system
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ da = a and a ⋅ 1 = a, however da ≠ 1
- Not right cancellative, because right multiplication by d is not injective:
-
da ⋅ d = d and 1 ⋅ d = d, however da ≠ 1
- Auxiliary generators:
- d = bc
- e = aaaab
- Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = deg(d) = 0, a < c < d; deg(e) = deg(b) = 1, e < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:aab=ba,abc=1 reversed:acd/eb bc=d,aaaab=e morph:2/2,5/1
ad=1
ea=aae
ec=aaa
aaed=e
eda=e
edc=a
edda=ed
eddc=d
b=edd
eed=edde