#2559 ⟨
a
,
b
|
aabbba
=
bbaa
⟩
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Monoid enumeration
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#2558
⟨
a
,
b
|
aabbba
=
babb
⟩
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#2560
⟨
a
,
b
|
aabbba
=
bbab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
a
2
b
3
⋅
a
=
b
2
a
2
and
b
2
a
⋅
a
=
b
2
a
2
, however
a
2
b
3
≠
b
2
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
Auxiliary generators:
c
=
bbba
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
bca
⇒
a
2
c
2
[5]
2.
b
a
2
c
⇒
ca
[4]
3.
b
2
a
2
⇒
a
2
c
[3]
4.
b
3
a
⇒
c
[2]
# ab:aabbba=bbaa ac/b bbba=c morph:4/3 bca=aacc baac=ca bbaa=aac bbba=c