#25102 ⟨
a
,
b
|
ab
=
a
,
bbbbaa
=
ba
⟩
Up:
Monoid enumeration
Prev:
#25100
⟨
a
,
b
|
ab
=
a
,
bbbbaa
=
aa
⟩
Next:
#25108
⟨
a
,
b
|
ab
=
a
,
bbbbba
=
aa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
b
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
a
is not injective:
a
2
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
a
2
≠
a
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
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
a
[1]
2.
a
3
⇒
a
2
[3]
3.
b
a
2
⇒
ba
[4]
4.
b
4
a
⇒
ba
[5]
# ab:ab=a,bbbbaa=ba ab - - ab=a aaa=aa baa=ba bbbba=ba