#2268 ⟨
a
,
b
,
c
|
abac
=1,
bcca
=1⟩
Up:
Monoid enumeration
Prev:
#2264
⟨
a
,
b
,
c
|
abac
=1,
baca
=1⟩
Next:
#2272
⟨
a
,
b
,
c
|
abac
=1,
caba
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
acab
=
b
and
b
⋅ 1 =
b
, however
acab
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
bc
⋅
c
=
bac
and
ba
⋅
c
=
bac
, however
bc
≠
ba
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
c
2
⇒
bac
[3]
2.
abac
⇒ 1
[1]
3.
baca
⇒ 1
[4]
# abc:abac=1,bcca=1 abc - - bcc=bac abac=1 baca=1