#14356 ⟨
a
,
b
|
aaaa
=
a
,
abbbb
=
b
⟩
Up:
Monoids with two generators and two relations
Prev:
#14355
⟨
a
,
b
|
aaaa
=
a
,
abbbb
=
a
⟩
Next:
#14357
⟨
a
,
b
|
aaaa
=
a
,
baaab
=
a
⟩
Properties
Presentation has sum-of-sides 11
Finite non-commutative monoid with 40 elements
Element profile
1 element center:
1
6 idempotent elements:
1,
a
3
,
b
3
a
,
b
6
a
2
,
b
9
,
b
9
a
3
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(
b
) = 0; deg(
a
) = 1
b
10
⇒
b
ab
⇒
b
7
a
4
⇒
a
# ab:aaaa=a,abbbb=b b/a bbbbbbbbbb=b ab=bbbbbbb aaaa=a
Right Cayley graph
Left Cayley graph
