#1073 ⟨a, b | aababa=baa⟩
Contents
- Properties
- Rewriting system
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not right cancellative, because right multiplication by a is not injective:
-
bd ⋅ a = cdba and cdb ⋅ a = cdba, however bd ≠ cdb
- Auxiliary generators:
- c = baa
- d = aba
- Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = deg(c) = 0, a < d < c; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aababa=baa reversed:adc/b baa=c,aba=d morph:3/1,3/0
ac=da
adc=ca
aba=d
adba=c
abd=dba
adbd=cba
bc=cbd
baa=c
bda=cdba
bad=cba
bdd=cdbd
bdc=cdcbd