#3369 ⟨
a
,
b
,
c
|
ab
=
aa
,
ccc
=
a
⟩
Up:
Monoid enumeration
Prev:
#3368
⟨
a
,
b
,
c
|
ab
=
aa
,
ccb
=
c
⟩
Next:
#3370
⟨
a
,
b
,
c
|
ab
=
aa
,
ccc
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
c
2
b
=
c
6
and
c
⋅
c
5
=
c
6
, however
c
2
b
≠
c
5
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 recursive path with deg(
c
) = 0; deg(
a
) = deg(
b
) = 1,
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
⇒
c
3
[2]
2.
c
3
b
⇒
c
6
[4]
# abc:ab=aa,ccc=a c/ab - - a=ccc cccb=cccccc