#2618 ⟨
a
,
b
|
abbaab
=
aabb
⟩
Up:
Monoid enumeration
Prev:
#2617
⟨
a
,
b
|
abbaab
=
aaba
⟩
Next:
#2619
⟨
a
,
b
|
abbaab
=
abaa
⟩
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
⋅
b
2
a
2
b
=
a
2
b
2
and
a
⋅
a
b
2
=
a
2
b
2
, however
b
2
a
2
b
≠
a
b
2
Not right cancellative, because right multiplication by
b
is not injective:
a
b
2
a
2
⋅
b
=
a
2
b
2
and
a
2
b
⋅
b
=
a
2
b
2
, however
a
b
2
a
2
≠
a
2
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
=
aab
Reduction order:
Left-to-right shortlex with
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
acb
⇒
cbc
[5]
2.
a
2
b
⇒
c
[2]
3.
a
b
2
c
⇒
cb
[4]
# ab:abbaab=aabb cab aab=c morph:3/0 acb=cbc aab=c abbc=cb