#4186 ⟨a, b, c | aab=1, abca=c⟩
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 ⋅ ea = a and a ⋅ 1 = a, however ea ≠ 1
- Not right cancellative, because right multiplication by e is not injective:
-
ea ⋅ e = e and 1 ⋅ e = e, however ea ≠ 1
- Auxiliary generators:
- d = cb
- e = ab
- Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(c) = deg(a) = deg(e) = 1, c < a < e; deg(b) = 2
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:aab=1,abca=c d/cae/b cb=d,ab=e morph:2/0,2/0
dc=cd
da=ad
de=ed
ce=ad
ac=ca
aad=c
ae=1
ec=ad
ead=d
db=eed
cb=d
ab=e