#3538 ⟨
a
,
b
,
c
|
bb
=
ac
,
caa
=
c
⟩
Up:
Monoid enumeration
Prev:
#3537
⟨
a
,
b
,
c
|
bb
=
ac
,
caa
=
b
⟩
Next:
#3539
⟨
a
,
b
,
c
|
bb
=
ac
,
cba
=
a
⟩
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
c
is not injective:
c
⋅
a
2
=
c
and
c
⋅ 1 =
c
, however
a
2
≠ 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 recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
c
a
2
⇒
c
[2]
2.
acb
⇒
bac
[3]
3.
c
2
b
⇒
cabac
[4]
4.
b
2
⇒
ac
[1]
# abc:bb=ac,caa=c ac/b - - caa=c acb=bac ccb=cabac bb=ac