#4359 ⟨
a
,
b
,
c
|
aab
=1,
ccca
=
c
⟩
Up:
Monoid enumeration
Prev:
#4356
⟨
a
,
b
,
c
|
aab
=1,
ccbc
=
c
⟩
Next:
#4360
⟨
a
,
b
,
c
|
aab
=1,
cccb
=
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
⋅
c
2
a
=
c
and
c
⋅ 1 =
c
, however
c
2
a
≠ 1
Not right cancellative, because right multiplication by
ab
is not injective:
aba
⋅
ab
=
ab
and 1 ⋅
ab
=
ab
, however
aba
≠ 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
3
a
⇒
c
[2]
2.
cb
⇒
c
5
[4]
3.
a
2
b
⇒ 1
[1]
4.
cab
⇒
c
3
[3]
# abc:aab=1,ccca=c ac/b - - ccca=c cb=ccccc aab=1 cab=ccc