#398 ⟨
a
,
b
|
abaabab
=
b
⟩
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Monoid enumeration
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#397
⟨
a
,
b
|
abaabab
=
a
⟩
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#399
⟨
a
,
b
|
abaabba
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
(
aba
)
2
⋅
b
=
b
and 1 ⋅
b
=
b
, however (
aba
)
2
≠ 1
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.
ba
(
ab
)
2
⇒
ab
a
2
b
2
[2]
2.
(
a
2
b
)
2
b
⇒
b
[3]
# ab:abaabab=b ab - - baabab=abaabb aabaabb=b