#14472 ⟨
a
,
b
|
aaab
=
a
,
bbbbb
=
b
⟩
Up:
Monoids with two generators and two relations
Prev:
#14469
⟨
a
,
b
|
aaab
=
a
,
bbbba
=
a
⟩
Next:
#14473
⟨
a
,
b
|
aaab
=
b
,
aaaaa
=
a
⟩
Properties
Presentation has sum-of-sides 11
Finite non-commutative monoid with 45 elements
Element profile
1 element center:
1
7 idempotent elements:
1,
b
a
2
,
b
4
,
b
2
a
4
,
a
8
,
b
3
a
6
,
b
4
a
8
Complete rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
1
1
Reduction order:
Left-to-right recursive path with deg(
a
) = 0; deg(
b
) = 1
a
9
⇒
a
ab
⇒
a
7
b
5
⇒
b
# ab:aaab=a,bbbbb=b a/b aaaaaaaaa=a ab=aaaaaaa bbbbb=b
Right Cayley graph
Left Cayley graph
