#3043 ⟨
a
,
b
|
aabaabbaabb
=1⟩
Up:
Monoid enumeration
Prev:
#3040
⟨
a
,
b
|
aabaababbba
=1⟩
Next:
#3045
⟨
a
,
b
|
aabaabbabab
=1⟩
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
⋅
ab
(
a
2
b
2
)
2
a
=
a
and
a
⋅ 1 =
a
, however
ab
(
a
2
b
2
)
2
a
≠ 1
Not right cancellative, because right multiplication by
ab
(
a
2
b
2
)
2
is not injective:
ab
(
a
2
b
2
)
2
a
⋅
ab
(
a
2
b
2
)
2
=
ab
(
a
2
b
2
)
2
and 1 ⋅
ab
(
a
2
b
2
)
2
=
ab
(
a
2
b
2
)
2
, however
ab
(
a
2
b
2
)
2
a
≠ 1
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
2
b
(
a
2
b
2
)
2
⇒ 1
[1]
# ab:aabaabbaabb=1 ab - - aabaabbaabb=1