#13180 ⟨
a
,
b
|
abb
=
aaa
,
baa
=
ba
⟩
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Monoid enumeration
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#13179
⟨
a
,
b
|
abb
=
aaa
,
baa
=
ab
⟩
Next:
#13181
⟨
a
,
b
|
abb
=
aaa
,
baa
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ab
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
a
2
=
ba
and
b
⋅
a
=
ba
, however
a
2
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
ba
⋅
a
=
ba
and
b
⋅
a
=
ba
, however
ba
≠
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
b
2
⇒
a
3
[1]
2.
b
a
2
⇒
ba
[2]
3.
a
5
⇒
a
4
[3]
# ab:abb=aaa,baa=ba ab - - abb=aaa baa=ba aaaaa=aaaa