#14339 ⟨
a
,
b
|
aaaa
=
a
,
aabab
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#14336
⟨
a
,
b
|
aaaa
=
a
,
aaabb
=
b
⟩
Next:
#14341
⟨
a
,
b
|
aaaa
=
a
,
aabba
=
a
⟩
Properties
Presentation has sum-of-sides 11
Infinite non-commutative monoid
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
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Auxiliary generator:
ab=c
a
3
⇒
c
2
a
c
2
⇒
a
c
2
a
⇒
a
c
3
⇒
c
ab
⇒
c
cb
⇒
c
a
2
c
# ab:aaaa=a,aabab=a ac/b ab=c frequency:2/0 aaa=cc acc=a cca=a ccc=c ab=c cb=caac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
