#4509 ⟨
a
,
b
|
aaababaa
=
aba
⟩
Up:
Monoid enumeration
Prev:
#4508
⟨
a
,
b
|
aaababaa
=
aab
⟩
Next:
#4510
⟨
a
,
b
|
aaababaa
=
abb
⟩
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
(
ab
)
2
a
2
=
aba
and
a
⋅
ba
=
aba
, however
a
(
ab
)
2
a
2
≠
ba
Not right cancellative, because right multiplication by
a
is not injective:
a
3
(
ba
)
2
⋅
a
=
aba
and
ab
⋅
a
=
aba
, however
a
3
(
ba
)
2
≠
ab
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
bab
a
2
⇒
aba
[1]
2.
a
3
(
ba
)
3
⇒ (
aba
)
2
b
a
2
[2]
# ab:aaababaa=aba ba - - aaababaa=aba aaabababa=abaababaa