#5394 ⟨
a
,
b
,
c
|
ab
=
a
,
bcbc
=
c
⟩
Up:
Monoid enumeration
Prev:
#5393
⟨
a
,
b
,
c
|
ab
=
a
,
bcbc
=
b
⟩
Next:
#5395
⟨
a
,
b
,
c
|
ab
=
a
,
bcca
=
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
⋅
b
=
a
and
a
⋅ 1 =
a
, however
b
≠ 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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
a
[1]
2.
a
c
2
⇒
ac
[5]
3.
cbc
⇒
b
c
2
[4]
4.
b
2
c
2
⇒
c
[6]
# abc:ab=a,bcbc=c abc - - ab=a acc=ac cbc=bcc bbcc=c