#1688 ⟨
a
,
b
,
c
|
aab
=
bb
,
cac
=1⟩
Up:
Monoid enumeration
Prev:
#1687
⟨
a
,
b
,
c
|
aab
=
bb
,
cab
=1⟩
Next:
#1689
⟨
a
,
b
,
c
|
aab
=
bb
,
cba
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
a
2
≠
b
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
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ca
[3]
2.
c
2
a
⇒ 1
[4]
3.
a
2
b
⇒
b
2
[1]
4.
c
2
b
2
⇒
ab
[5]
# abc:aab=bb,cac=1 cab - - ac=ca cca=1 aab=bb ccbb=ab