#3760 ⟨
a
,
b
|
ababaaabba
=
b
⟩
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Monoid enumeration
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#3759
⟨
a
,
b
|
ababaaabba
=
a
⟩
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#3761
⟨
a
,
b
|
ababaabaab
=
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
|
aabbab
-1
aba
-1
b
⟩
Embedding:
φ
(
a
) =
b
,
φ
(
b
) =
b
-1
a
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.
(
ab
)
2
a
3
b
3
⇒
b
2
ab
a
3
b
2
a
[2]
2.
(
ab
)
2
a
3
b
2
a
⇒
b
[1]
# ab:ababaaabba=b ba - - ababaaabbb=bbabaaabba ababaaabba=b