#16422 ⟨
a
,
b
|
aba
=
ab
,
bbaa
=
ab
⟩
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Monoid enumeration
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#16421
⟨
a
,
b
|
aba
=
ab
,
bbaa
=
aa
⟩
Next:
#16423
⟨
a
,
b
|
aba
=
ab
,
bbaa
=
ba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ba
=
ab
and
a
⋅
b
=
ab
, however
ba
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
ab
⋅
b
=
a
2
b
and
a
2
⋅
b
=
a
2
b
, however
ab
≠
a
2
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.
aba
⇒
ab
[1]
2.
a
b
2
⇒
a
2
b
[4]
3.
a
3
b
⇒
a
2
b
[5]
4.
b
2
a
2
⇒
ab
[2]
# ab:aba=ab,bbaa=ab ab - - aba=ab abb=aab aaab=aab bbaa=ab