#513 ⟨
a
,
b
|
aaabb
=
bba
⟩
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Monoid enumeration
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#512
⟨
a
,
b
|
aaabb
=
bab
⟩
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#514
⟨
a
,
b
|
aaabb
=
bbb
⟩
Contents
Properties
Rewriting system
Other submonoids of same group
Properties
Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaabba
-1
b
-1
b
-1
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
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
3
b
2
⇒
b
2
a
[1]
# ab:aaabb=bba ab - - aaabb=bba
Other submonoids of same group
2 unique, 2 total
Σ
#
Presentation
Properties
10
2241
⟨
a
,
b
|
aababab
=
baa
⟩
Can
Inf
10
2447
⟨
a
,
b
|
aaabab
=
baba
⟩
Can
Inf