#2591 ⟨
a
,
b
|
ababab
=
aaba
⟩
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Monoid enumeration
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#2590
⟨
a
,
b
|
ababab
=
aaab
⟩
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#2592
⟨
a
,
b
|
ababab
=
aabb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
(
ab
)
2
=
a
2
ba
and
a
⋅
aba
=
a
2
ba
, however
b
(
ab
)
2
≠
aba
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(
c
) = 0; deg(
a
) = deg(
b
) = 1,
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
c
4
a
⇒
a
c
4
[6]
2.
c
3
b
⇒
a
c
2
[5]
3.
aca
⇒
c
3
[4]
4.
ab
⇒
c
[2]
# ab:ababab=aaba c/ab ab=c morph:2/0 cccca=acccc cccb=acc aca=ccc ab=c