#16543 ⟨
a
,
b
|
aba
=
ab
,
bbb
=
aba
⟩
Up:
Monoid enumeration
Prev:
#16540
⟨
a
,
b
|
aba
=
ab
,
bba
=
aaa
⟩
Next:
#16544
⟨
a
,
b
|
aba
=
ba
,
baa
=
aba
⟩
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
⋅
b
2
a
=
b
3
and
b
⋅
b
2
=
b
3
, however
b
2
a
≠
b
2
Not right cancellative, because right multiplication by
b
is not injective:
a
⋅
b
=
b
3
and
b
2
⋅
b
=
b
3
, however
a
≠
b
2
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
6
⇒
b
4
[5]
2.
ab
⇒
b
3
[2]
3.
b
3
a
⇒
b
3
[4]
# ab:aba=ab,bbb=aba b/a - - bbbbbb=bbbb ab=bbb bbba=bbb