#513 ⟨
a
,
b
,
c
|
ab
=
aa
,
ca
=
c
⟩
Up:
Monoid enumeration
Prev:
#512
⟨
a
,
b
,
c
|
ab
=
aa
,
ca
=
b
⟩
Next:
#514
⟨
a
,
b
,
c
|
ab
=
aa
,
cb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
a
=
c
and
c
⋅ 1 =
c
, however
a
≠ 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
2
[1]
2.
ca
⇒
c
[2]
3.
cb
⇒
c
[3]
# abc:ab=aa,ca=c abc - - ab=aa ca=c cb=c