#1355 ⟨a, b, c | ab=1, bbca=c⟩
Contents
- Properties
- Rewriting system
- Sum of relation sides is 7
- 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 = ad
- Reduction order:
- Right-to-left recursive path with deg(b) = 0; deg(c) = deg(d) = deg(a) = deg(e) = 1, c < d < a < e
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:ab=1,bbca=c reversed:b/cdae ac=d,ad=e morph:2/0,2/0
cb=bbc
bd=c
db=bc
ab=1
be=d
eb=c
ac=d
cd=ec
ad=e
ca=e
ce=ed
ae=da