#2878 ⟨
a
,
b
|
aaaabbabaab
=1⟩
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Monoid enumeration
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#2876
⟨
a
,
b
|
aaaabbaabbb
=1⟩
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#2880
⟨
a
,
b
|
aaaabbababb
=1⟩
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
⋅
a
3
b
2
(
aba
)
2
=
a
and
a
⋅ 1 =
a
, however
a
3
b
2
(
aba
)
2
≠ 1
Not right cancellative, because right multiplication by
a
3
b
2
ab
a
2
b
is not injective:
a
3
b
2
(
aba
)
2
⋅
a
3
b
2
ab
a
2
b
=
a
3
b
2
ab
a
2
b
and 1 ⋅
a
3
b
2
ab
a
2
b
=
a
3
b
2
ab
a
2
b
, however
a
3
b
2
(
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.
a
4
b
2
ab
a
2
b
⇒ 1
[1]
# ab:aaaabbabaab=1 ab - - aaaabbabaab=1