#2484 ⟨
a
,
b
|
aabaab
=
abab
⟩
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Monoid enumeration
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#2483
⟨
a
,
b
|
aabaab
=
abaa
⟩
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#2485
⟨
a
,
b
|
aabaab
=
abba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
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
= (
ab
)
2
and
a
⋅
bab
= (
ab
)
2
, however
ab
a
2
b
≠
bab
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
a
2
⋅
b
= (
ab
)
2
and
aba
⋅
b
= (
ab
)
2
, however
a
2
b
a
2
≠
aba
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
2
b
)
2
⇒ (
ab
)
2
[1]
2.
a
(
ab
)
3
⇒ (
ab
)
2
a
2
b
[2]
# ab:aabaab=abab ba - - aabaab=abab aababab=ababaab