#12238 ⟨
a
,
b
|
aaab
=
aa
,
bbba
=
a
⟩
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Monoid enumeration
Prev:
#12236
⟨
a
,
b
|
aaab
=
aa
,
bbab
=
a
⟩
Next:
#12240
⟨
a
,
b
|
aaab
=
aa
,
bbbb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
4
=
a
2
and
a
⋅
a
=
a
2
, however
a
4
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
b
3
⋅
a
=
a
and 1 ⋅
a
=
a
, however
b
3
≠ 1
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
5
⇒
a
2
[6]
2.
a
2
b
⇒
a
4
[7]
3.
b
3
a
⇒
a
[2]
# ab:aaab=aa,bbba=a a/b - - aaaaa=aa aab=aaaa bbba=a