#6747 ⟨
a
,
b
|
aba
=
a
,
abba
=
bb
⟩
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Monoid enumeration
Prev:
#6746
⟨
a
,
b
|
aba
=
a
,
abba
=
ab
⟩
Next:
#6748
⟨
a
,
b
|
aba
=
a
,
abbb
=
aa
⟩
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
and
a
⋅ 1 =
a
, however
ba
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
ab
⋅
a
=
a
and 1 ⋅
a
=
a
, however
ab
≠ 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 shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
a
⇒
b
3
[8]
2.
a
b
2
⇒
b
3
[9]
3.
aba
⇒
a
[1]
4.
b
4
⇒
b
2
[7]
# ab:aba=a,abba=bb ba - - bba=bbb abb=bbb aba=a bbbb=bb