#2990 ⟨
a
,
b
,
c
|
aab
=
c
,
bcb
=
c
⟩
Up:
Monoid enumeration
Prev:
#2988
⟨
a
,
b
,
c
|
aab
=
c
,
bcb
=
a
⟩
Next:
#2991
⟨
a
,
b
,
c
|
aab
=
c
,
bcc
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
2
⋅
c
=
b
c
2
and
bc
⋅
c
=
b
c
2
, however
a
2
≠
bc
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
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
bcb
⇒
c
[2]
2.
a
2
b
⇒
c
[1]
3.
a
2
c
⇒
b
c
2
[4]
4.
c
2
b
⇒
b
c
2
[3]
# abc:aab=c,bcb=c bac - - bcb=c aab=c aac=bcc ccb=bcc