#5238 ⟨
a
,
b
|
aba
=
aa
,
babb
=
a
⟩
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Monoid enumeration
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#5237
⟨
a
,
b
|
aba
=
aa
,
baab
=
b
⟩
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#5239
⟨
a
,
b
|
aba
=
aa
,
babb
=
b
⟩
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
⋅
ba
=
a
2
and
a
⋅
a
=
a
2
, however
ba
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
ab
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
ab
≠
a
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
⇒
a
2
[1]
2.
b
a
2
⇒
a
2
[4]
3.
a
2
b
2
⇒
a
2
[3]
4.
ba
b
2
⇒
a
[2]
# ab:aba=aa,babb=a ab - - aba=aa baa=aa aabb=aa babb=a