#7486 ⟨a, b, c | ab=1, baca=ac⟩
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 ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 1
- Auxiliary generators:
- d = ac
- e = db
- Reduction order:
- Left-to-right shortlex with d < a < b < e < c
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:ab=1,baca=ac dabec ac=d,db=e morph:2/0,2/0
db=e
dc=de
ad=da
ab=1
ae=d
ac=d
bd=e
ed=de
ea=d
eb=be
ec=ee