#4275 ⟨
a
,
b
,
c
|
aab
=1,
bcbc
=
c
⟩
Up:
Monoid enumeration
Prev:
#4272
⟨
a
,
b
,
c
|
aab
=1,
bcbb
=
c
⟩
Next:
#4278
⟨
a
,
b
,
c
|
aab
=1,
bcca
=
c
⟩
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
⋅
aba
=
a
and
a
⋅ 1 =
a
, however
aba
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
b
2
c
⋅
c
=
c
and 1 ⋅
c
=
c
, however
b
2
c
≠ 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
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒ 1
[1]
2.
a
2
c
⇒
b
c
2
[4]
3.
cbc
⇒
b
c
2
[5]
4.
b
2
c
2
⇒
c
[6]
# abc:aab=1,bcbc=c bac - - aab=1 aac=bcc cbc=bcc bbcc=c