#16078 ⟨
a
,
b
|
aaa
=
bb
,
bbbb
=
aa
⟩
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Monoid enumeration
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#16073
⟨
a
,
b
|
aaa
=
bb
,
baab
=
bb
⟩
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#16079
⟨
a
,
b
|
aaa
=
bb
,
bbbb
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ab
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
5
=
a
2
and
a
⋅
a
=
a
2
, however
a
5
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
a
5
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
a
5
≠
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
6
⇒
a
2
[2]
2.
ab
a
2
⇒
b
a
3
[5]
3.
a
2
b
⇒
b
a
2
[4]
4.
b
2
⇒
a
3
[1]
# ab:aaa=bb,bbbb=aa a/b - - aaaaaa=aa abaa=baaa aab=baa bb=aaa