#2370 ⟨
a
,
b
,
c
|
aab
=
a
,
bacb
=1⟩
Up:
Monoid enumeration
Prev:
#2368
⟨
a
,
b
,
c
|
aab
=
a
,
babc
=1⟩
Next:
#2371
⟨
a
,
b
,
c
|
aab
=
a
,
bacc
=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
a
is not injective:
a
⋅
ab
=
a
and
a
⋅ 1 =
a
, however
ab
≠ 1
Not right cancellative, because right multiplication by
c
b
2
is not injective:
c
b
2
a
⋅
c
b
2
=
c
b
2
and 1 ⋅
c
b
2
=
c
b
2
, however
c
b
2
a
≠ 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
⇒
a
3
[5]
3.
bac
⇒
acb
[4]
4.
ac
b
2
⇒ 1
[6]
# abc:aab=a,bacb=1 abc - - aab=a aac=aaa bac=acb acbb=1