#6710 ⟨
a
,
b
|
aab
=
b
,
bbaa
=
aa
⟩
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Monoid enumeration
Prev:
#6709
⟨
a
,
b
|
aab
=
b
,
babb
=
bb
⟩
Next:
#6712
⟨
a
,
b
|
aab
=
b
,
bbaa
=
ba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
b
2
=
b
and
b
⋅ 1 =
b
, however
b
2
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
2
≠ 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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒
b
[1]
2.
b
3
⇒
b
[4]
3.
a
4
⇒
a
2
[3]
4.
b
2
a
2
⇒
a
2
[2]
5.
b
2
ab
⇒
ab
[5]
# ab:aab=b,bbaa=aa ab - - aab=b bbb=b aaaa=aa bbaa=aa bbab=ab