#3469 ⟨
a
,
b
,
c
|
ba
=
ac
,
bcb
=
a
⟩
Up:
Monoid enumeration
Prev:
#3468
⟨
a
,
b
,
c
|
ba
=
ac
,
bbc
=
c
⟩
Next:
#3470
⟨
a
,
b
,
c
|
ba
=
ac
,
bcb
=
b
⟩
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
⋅
ab
=
bca
and
b
⋅
ca
=
bca
, however
ab
≠
ca
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
<
c
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ba
[1]
2.
bcb
⇒
a
[2]
3.
bab
⇒
bca
[3]
4.
a
2
b
⇒
b
a
2
[4]
# abc:ba=ac,bcb=a bca - - ac=ba bcb=a bab=bca aab=baa