#16123 ⟨
a
,
b
|
aab
=
aa
,
baba
=
ba
⟩
Up:
Monoid enumeration
Prev:
#16121
⟨
a
,
b
|
aab
=
aa
,
baba
=
aa
⟩
Next:
#16124
⟨
a
,
b
|
aab
=
aa
,
baba
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
b
2
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ab
=
a
2
and
a
⋅
a
=
a
2
, however
ab
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
bab
⋅
a
=
ba
and
b
⋅
a
=
ba
, however
bab
≠
b
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.
a
2
b
⇒
a
2
[1]
2.
a
4
⇒
a
3
[3]
3.
(
ba
)
2
⇒
ba
[2]
# ab:aab=aa,baba=ba ab - - aab=aa aaaa=aaa baba=ba