#13043 ⟨
a
,
b
|
abb
=
aba
,
bbbb
=
b
⟩
Up:
Monoid enumeration
Prev:
#13040
⟨
a
,
b
|
abb
=
aba
,
bbba
=
a
⟩
Next:
#13049
⟨
a
,
b
|
baa
=
aab
,
aaba
=
b
⟩
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
3
=
b
and
b
⋅ 1 =
b
, however
b
3
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
b
3
⋅
b
=
b
and 1 ⋅
b
=
b
, 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 shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
⇒
a
b
2
[1]
2.
b
4
⇒
b
[2]
3.
a
b
2
a
⇒
a
b
3
[4]
4.
a
b
3
a
⇒
ab
[3]
# ab:abb=aba,bbbb=b ba - - aba=abb bbbb=b abba=abbb abbba=ab