#4066 ⟨
a
,
b
|
aabaaaaba
=
ab
⟩
Up:
Monoid enumeration
Prev:
#4065
⟨
a
,
b
|
aabaaaaba
=
aa
⟩
Next:
#4067
⟨
a
,
b
|
aabaaaaba
=
ba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ab
a
4
ba
=
ab
and
a
⋅
b
=
ab
, however
ab
a
4
ba
≠
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
=
aaba
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.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
c
2
a
⇒
a
c
2
[6]
2.
a
(
ca
)
2
⇒
c
[4]
3.
ab
⇒
cac
[3]
4.
cb
⇒
ac
a
2
c
3
[7]
# ab:aabaaaaba=ab ac/b aaba=c morph:4/0 cca=acc acaca=c ab=cac cb=acaaccc