#4788 ⟨
a
,
b
|
abaabaab
=
bab
⟩
Up:
Monoid enumeration
Prev:
#4787
⟨
a
,
b
|
abaabaab
=
baa
⟩
Next:
#4789
⟨
a
,
b
|
abaabaab
=
bba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
(
ca
)
2
⋅
c
=
c
2
and
c
⋅
c
=
c
2
, however
a
(
ca
)
2
≠
c
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.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
c
3
⇒
c
2
ac
[6]
2.
(
ac
)
3
⇒
c
2
[5]
3.
bc
⇒
c
(
ac
)
2
[4]
4.
ab
⇒
c
[2]
# ab:abaabaab=bab ca/b ab=c morph:2/0 accc=ccac acacac=cc bc=cacac ab=c