#2710 ⟨
a
,
b
|
abbab
=
ababa
⟩
Up:
Monoid enumeration
Prev:
#2709
⟨
a
,
b
|
abbab
=
abaab
⟩
Next:
#2711
⟨
a
,
b
|
abbab
=
abbaa
⟩
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
c
is not injective:
c
⋅
ca
=
cbc
and
c
⋅
bc
=
cbc
, however
ca
≠
bc
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 shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ab
⇒
c
[2]
2.
c
2
a
⇒
cbc
[4]
3.
(
cb
)
2
⇒
c
3
[5]
4.
c
4
b
⇒
cb
c
3
[6]
# ab:abbab=ababa abc ab=c morph:2/0 ab=c cca=cbc cbcb=ccc ccccb=cbccc