#5272 ⟨
a
,
b
|
aabbbba
=
abbb
⟩
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Monoid enumeration
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#5271
⟨
a
,
b
|
aabbbba
=
abba
⟩
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#5273
⟨
a
,
b
|
aabbbba
=
baaa
⟩
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
b
4
a
=
a
b
3
and
a
⋅
b
3
=
a
b
3
, however
a
b
4
a
≠
b
3
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
Auxiliary generators:
c
=
abbb
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
3
⇒
c
[2]
2.
acba
⇒
c
[4]
3.
c
b
3
⇒
acbc
[5]
4.
c
2
ba
⇒
acbc
[6]
# ab:aabbbba=abbb abc abbb=c magic:0 abbb=c acba=c cbbb=acbc ccba=acbc