#4794 ⟨
a
,
b
|
abaababa
=
abb
⟩
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Monoid enumeration
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#4793
⟨
a
,
b
|
abaababa
=
aba
⟩
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#4795
⟨
a
,
b
|
abaababa
=
baa
⟩
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
c
is not injective:
c
⋅
b
=
ca
c
2
a
and
c
⋅
a
c
2
a
=
ca
c
2
a
, however
b
≠
a
c
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
=
ab
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.
ab
⇒
c
[2]
2.
cb
⇒
ca
c
2
a
[4]
# ab:abaababa=abb ac/b ab=c morph:2/1 ab=c cb=cacca