#13139 ⟨
a
,
b
|
aab
=
aaa
,
bba
=
bb
⟩
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Monoid enumeration
Prev:
#13138
⟨
a
,
b
|
aab
=
aaa
,
bba
=
ba
⟩
Next:
#13140
⟨
a
,
b
|
aab
=
aaa
,
bbb
=
aa
⟩
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
b
is not injective:
b
⋅
b
2
=
b
2
and
b
⋅
b
=
b
2
, however
b
2
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
b
2
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
b
2
≠
b
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
3
⇒
b
2
[4]
2.
b
2
a
⇒
b
2
[2]
3.
a
3
⇒
a
2
b
[1]
4.
a
2
ba
⇒
a
2
b
2
[3]
# ab:aab=aaa,bba=bb ba - - bbb=bb bba=bb aaa=aab aaba=aabb