#1186 ⟨
a
,
b
|
aaabb
=
abab
⟩
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Monoid enumeration
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#1185
⟨
a
,
b
|
aaabb
=
abaa
⟩
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#1187
⟨
a
,
b
|
aaabb
=
abba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
2
b
2
= (
ab
)
2
and
a
⋅
bab
= (
ab
)
2
, however
a
2
b
2
≠
bab
Not right cancellative, because right multiplication by
b
is not injective:
a
3
b
⋅
b
= (
ab
)
2
and
aba
⋅
b
= (
ab
)
2
, however
a
3
b
≠
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
b
2
⇒ (
ab
)
2
[1]
# ab:aaabb=abab ab - - aaabb=abab