#4053 ⟨
a
,
b
|
abb
=
aaa
,
bbbb
=1⟩
Up:
Monoid enumeration
Prev:
#4037
⟨
a
,
b
|
aba
=
aab
,
bbbb
=1⟩
Next:
#4079
⟨
a
,
b
|
abb
=
aba
,
bbbb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
3
ba
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
4
=
a
and
a
⋅ 1 =
a
, however
a
4
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
4
⋅
a
=
a
and 1 ⋅
a
=
a
, however
a
4
≠ 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
b
2
⇒
a
3
[1]
2.
b
4
⇒ 1
[2]
3.
a
5
⇒
a
[3]
# ab:abb=aaa,bbbb=1 ab - - abb=aaa bbbb=1 aaaaa=a