#4708 ⟨
a
,
b
|
aabbabba
=
aab
⟩
Up:
Monoid enumeration
Prev:
#4707
⟨
a
,
b
|
aabbabba
=
aaa
⟩
Next:
#4709
⟨
a
,
b
|
aabbabba
=
aba
⟩
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
⋅
a
(
ca
)
2
b
=
a
2
c
and
a
⋅
ac
=
a
2
c
, however
a
(
ca
)
2
b
≠
ac
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
=
bb
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.
cb
⇒
bc
[4]
2.
a
2
b
⇒
a
2
(
ca
)
2
[3]
3.
a
2
(
ca
)
2
b
⇒
a
2
c
[5]
4.
b
2
⇒
c
[2]
# ab:aabbabba=aab ac/b bb=c morph:2/2 cb=bc aab=aacaca aacacab=aac bb=c