#281 ⟨
a
,
b
,
c
|
aab
=
a
,
aac
=1⟩
Up:
Monoid enumeration
Prev:
#279
⟨
a
,
b
,
c
|
aaa
=
b
,
cbc
=1⟩
Next:
#282
⟨
a
,
b
,
c
|
aab
=
a
,
abc
=1⟩
Contents
Properties
Rewriting system
Properties
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
⋅
ab
=
a
and
a
⋅ 1 =
a
, however
ab
≠ 1
Not right cancellative, because right multiplication by
ac
is not injective:
aca
⋅
ac
=
ac
and 1 ⋅
ac
=
ac
, however
aca
≠ 1
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.
a
2
b
⇒
a
[1]
2.
a
2
c
⇒ 1
[2]
# abc:aab=a,aac=1 abc - - aab=a aac=1