#5075 ⟨
a
,
b
|
aaabbaa
=
abba
⟩
Up:
Monoid enumeration
Prev:
#5074
⟨
a
,
b
|
aaabbaa
=
abab
⟩
Next:
#5076
⟨
a
,
b
|
aaabbaa
=
abbb
⟩
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
2
b
2
a
2
=
a
b
2
a
and
a
⋅
b
2
a
=
a
b
2
a
, however
a
2
b
2
a
2
≠
b
2
a
Not right cancellative, because right multiplication by
a
is not injective:
a
3
b
2
a
⋅
a
=
a
b
2
a
and
a
b
2
⋅
a
=
a
b
2
a
, however
a
3
b
2
a
≠
a
b
2
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
Reduction order:
Left-to-right shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
b
2
a
2
⇒
a
b
2
a
[1]
2.
a
3
(
b
2
a
)
2
⇒
a
(
b
2
a
2
)
2
[2]
# ab:aaabbaa=abba ba - - aaabbaa=abba aaabbabba=abbaabbaa