#3493 ⟨
a
,
b
|
aaabbaabba
=
b
⟩
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Monoid enumeration
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#3492
⟨
a
,
b
|
aaabbaabba
=
a
⟩
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#3494
⟨
a
,
b
|
aaabbaabbb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaabab
-1
b
-1
aab
-1
b
-1
⟩
Anti-isomorphic embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
-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
3
b
2
a
2
b
3
⇒
b
(
a
2
b
2
)
2
a
[2]
2.
a
(
a
2
b
2
)
2
a
⇒
b
[1]
# ab:aaabbaabba=b ba - - aaabbaabbb=baabbaabba aaabbaabba=b