#1886 ⟨
a
,
b
|
aaabaaba
=
ab
⟩
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Monoid enumeration
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#1885
⟨
a
,
b
|
aaabaaba
=
aa
⟩
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#1887
⟨
a
,
b
|
aaabaaba
=
ba
⟩
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
2
b
)
2
a
=
ab
and
a
⋅
b
=
ab
, however (
a
2
b
)
2
a
≠
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
ca
c
2
⇒ (
ca
)
3
[6]
2.
a
2
(
ca
)
2
⇒
c
[4]
3.
cb
⇒ (
ca
)
3
[7]
4.
ab
⇒
c
[2]
# ab:aaabaaba=ab ca/b ab=c magic:0 aacacc=cacaca aacaca=c cb=cacaca ab=c