#5310 ⟨
a
,
b
|
abaabab
=
aabb
⟩
Up:
Monoid enumeration
Prev:
#5309
⟨
a
,
b
|
abaabab
=
aaba
⟩
Next:
#5311
⟨
a
,
b
|
abaabab
=
abaa
⟩
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
⋅
ba
(
ab
)
2
=
a
2
b
2
and
a
⋅
a
b
2
=
a
2
b
2
, however
ba
(
ab
)
2
≠
a
b
2
Not right cancellative, because right multiplication by
b
is not injective:
(
aba
)
2
⋅
b
=
a
2
b
2
and
a
2
b
⋅
b
=
a
2
b
2
, however (
aba
)
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
Reduction order:
Left-to-right shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
aba
)
2
b
⇒
a
2
b
2
[1]
2.
a
(
b
a
2
)
2
b
2
⇒
a
2
b
2
a
(
ab
)
2
[2]
# ab:abaabab=aabb ab - - abaabab=aabb abaabaabb=aabbaabab