#16271 ⟨
a
,
b
|
aab
=
ba
,
bbbb
=
ba
⟩
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Monoid enumeration
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#16270
⟨
a
,
b
|
aab
=
ba
,
bbbb
=
ab
⟩
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#16272
⟨
a
,
b
|
aab
=
ba
,
bbbb
=
bb
⟩
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
b
is not injective:
b
⋅
a
=
b
4
and
b
⋅
b
3
=
b
4
, however
a
≠
b
3
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
b
4
and
b
3
⋅
b
=
b
4
, however
a
2
≠
b
3
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
8
⇒
b
5
[4]
2.
ba
⇒
b
4
[2]
3.
a
2
b
⇒
b
4
[3]
# ab:aab=ba,bbbb=ba b/a - - bbbbbbbb=bbbbb ba=bbbb aab=bbbb