#987 ⟨
a
,
b
|
abababa
=
ab
⟩
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Monoid enumeration
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#986
⟨
a
,
b
|
abababa
=
aa
⟩
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#988
⟨
a
,
b
|
abababa
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
c
2
a
=
c
and
c
⋅ 1 =
c
, however
c
2
a
≠ 1
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.
#
Rule
Proof
1.
c
3
a
⇒
c
[4]
2.
ab
⇒
c
[2]
3.
cb
⇒
c
4
[5]
# ab:abababa=ab ac/b ab=c magic:0 ccca=c ab=c cb=cccc