#1948 ⟨
a
,
b
|
aabaabaa
=
ab
⟩
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Monoid enumeration
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#1947
⟨
a
,
b
|
aabaabaa
=
aa
⟩
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#1949
⟨
a
,
b
|
aabaabaa
=
bb
⟩
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
⋅
a
(
b
a
2
)
2
=
ab
and
a
⋅
b
=
ab
, however
a
(
b
a
2
)
2
≠
b
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.
(
ac
)
2
a
2
⇒
c
[4]
2.
c
2
ac
a
2
⇒ (
ac
)
3
[6]
3.
ab
⇒
c
[2]
4.
cb
⇒ (
ac
)
3
[5]
# ab:aabaabaa=ab ac/b ab=c magic:0 acacaa=c ccacaa=acacac ab=c cb=acacac