#5426 ⟨
a
,
b
|
aaaaaa
=
ababa
⟩
Up:
Monoid enumeration
Prev:
#5425
⟨
a
,
b
|
aaaaaa
=
abaab
⟩
Next:
#5427
⟨
a
,
b
|
aaaaaa
=
ababb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
3
b
a
2
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
5
=
a
(
ba
)
2
and
a
⋅ (
ba
)
2
=
a
(
ba
)
2
, however
a
5
≠ (
ba
)
2
Not right cancellative, because right multiplication by
a
is not injective:
a
5
⋅
a
=
a
(
ba
)
2
and (
ab
)
2
⋅
a
=
a
(
ba
)
2
, however
a
5
≠ (
ab
)
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
6
⇒
a
(
ba
)
2
[1]
2.
(
ab
)
2
a
2
⇒
a
2
(
ba
)
2
[2]
# ab:aaaaaa=ababa ab - - aaaaaa=ababa ababaa=aababa