#5888 ⟨
a
,
b
,
c
|
ab
=
a
,
bcb
=
aa
⟩
Up:
Monoid enumeration
Prev:
#5887
⟨
a
,
b
,
c
|
ab
=
a
,
bca
=
cc
⟩
Next:
#5890
⟨
a
,
b
,
c
|
ab
=
a
,
bcb
=
ac
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ca
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
b
is not injective:
bcb
⋅
b
=
bcb
and
bc
⋅
b
=
bcb
, however
bcb
≠
bc
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 recursive path with deg(
b
) = 0; deg(
c
) = deg(
a
) = 1,
c
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
bc
b
2
⇒
bcb
[3]
2.
ab
⇒
a
[1]
3.
acb
⇒
bcba
[4]
4.
a
2
⇒
bcb
[2]
# abc:ab=a,bcb=aa b/ca - - bcbb=bcb ab=a acb=bcba aa=bcb