#2747 ⟨
a
,
b
,
c
|
abc
=
a
,
ccab
=1⟩
Up:
Monoid enumeration
Prev:
#2745
⟨
a
,
b
,
c
|
abc
=
a
,
cbcc
=1⟩
Next:
#2750
⟨
a
,
b
,
c
|
abc
=
a
,
ccbb
=1⟩
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
⋅
bc
=
c
and
c
⋅ 1 =
c
, however
bc
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
bc
⋅
b
=
b
and 1 ⋅
b
=
b
, however
bc
≠ 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.
cb
⇒ 1
[5]
2.
abc
⇒
a
[1]
3.
aca
⇒
a
[4]
4.
c
2
a
⇒
c
[3]
# abc:abc=a,ccab=1 abc - - cb=1 abc=a aca=a cca=c