#3064 ⟨
a
,
b
,
c
|
abc
=
a
,
bca
=
c
⟩
Up:
Monoid enumeration
Prev:
#3063
⟨
a
,
b
,
c
|
abc
=
a
,
bca
=
b
⟩
Next:
#3065
⟨
a
,
b
,
c
|
abc
=
a
,
cab
=
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
a
is not injective:
a
⋅
bc
=
a
and
a
⋅ 1 =
a
, however
bc
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
cb
⋅
c
=
c
and 1 ⋅
c
=
c
, however
cb
≠ 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.
ac
⇒
a
2
[3]
2.
c
2
⇒
ca
[5]
3.
abc
⇒
a
[1]
4.
bca
⇒
c
[2]
5.
cbc
⇒
c
[4]
# abc:abc=a,bca=c abc - - ac=aa cc=ca abc=a bca=c cbc=c