#5104 ⟨
a
,
b
|
aaabbba
=
aabb
⟩
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Monoid enumeration
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#5103
⟨
a
,
b
|
aaabbba
=
aaba
⟩
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#5105
⟨
a
,
b
|
aaabbba
=
abaa
⟩
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
2
b
3
a
=
a
2
b
2
and
a
⋅
a
b
2
=
a
2
b
2
, however
a
2
b
3
a
≠
a
b
2
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
=
aabb
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
2
⇒
c
[2]
2.
acba
⇒
c
[4]
3.
ca
b
2
⇒
acbc
[5]
4.
c
2
ba
⇒
acbc
[6]
# ab:aaabbba=aabb abc aabb=c magic:0 aabb=c acba=c cabb=acbc ccba=acbc