#500 ⟨
a
,
b
|
aaaba
=
aab
⟩
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Monoid enumeration
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#499
⟨
a
,
b
|
aaaba
=
aaa
⟩
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#501
⟨
a
,
b
|
aaaba
=
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
⋅
a
2
ba
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however
a
2
ba
≠
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
=
aab
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.
#
Rule
Proof
1.
aca
⇒
c
[4]
2.
c
2
a
⇒
a
c
2
[5]
3.
cb
⇒
a
2
c
2
[7]
4.
a
2
b
⇒
c
[2]
5.
cab
⇒
a
c
2
[6]
# ab:aaaba=aab ac/b aab=c magic:0 aca=c cca=acc cb=aacc aab=c cab=acc