#546 ⟨
a
,
b
|
ababa
=
aab
⟩
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Monoid enumeration
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#545
⟨
a
,
b
|
ababa
=
aaa
⟩
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#547
⟨
a
,
b
|
ababa
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
ba
)
2
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however (
ba
)
2
≠
ab
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:
Right-to-left recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 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.
ac
⇒
c
2
a
[4]
# ab:ababa=aab reversed:bc/a ab=c morph:2/0 ab=c ac=cca