#3068 ⟨
a
,
b
,
c
|
abc
=
a
,
cba
=
b
⟩
Up:
Monoid enumeration
Prev:
#3067
⟨
a
,
b
,
c
|
abc
=
a
,
cba
=
a
⟩
Next:
#3069
⟨
a
,
b
,
c
|
abc
=
a
,
cba
=
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
b
is not injective:
b
⋅
bc
=
b
and
b
⋅ 1 =
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
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
a
⇒
b
3
[5]
2.
b
2
c
⇒
b
[4]
3.
aba
⇒
a
b
2
[3]
4.
abc
⇒
a
[1]
5.
cba
⇒
b
[2]
# abc:abc=a,cba=b bac - - bba=bbb bbc=b aba=abb abc=a cba=b