#1688 ⟨
a
,
b
|
aababaaab
=
b
⟩
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Monoid enumeration
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#1687
⟨
a
,
b
|
aababaaab
=
a
⟩
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#1689
⟨
a
,
b
|
aababaaba
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
a
(
ab
)
2
a
3
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
(
ab
)
2
a
3
≠ 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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
(
ab
)
3
⇒
bab
a
3
b
[2]
2.
a
(
ab
)
2
a
3
b
⇒
b
[1]
# ab:aababaaab=b ba - - aababab=babaaab aababaaab=b