#6087 ⟨
a
,
b
,
c
|
ab
=
c
,
bca
=
bc
⟩
Up:
Monoid enumeration
Prev:
#6082
⟨
a
,
b
,
c
|
ab
=
c
,
bbc
=
cc
⟩
Next:
#6088
⟨
a
,
b
,
c
|
ab
=
c
,
bca
=
cc
⟩
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
⋅
ca
=
c
2
and
c
⋅
c
=
c
2
, however
ca
≠
c
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
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
c
[1]
2.
c
2
a
⇒
c
2
[3]
3.
c
2
b
⇒
c
3
[5]
4.
bca
⇒
bc
[2]
5.
bcb
⇒
b
c
2
[4]
# abc:ab=c,bca=bc acb - - ab=c cca=cc ccb=ccc bca=bc bcb=bcc