#6270 ⟨
a
,
b
|
aaa
=
a
,
babab
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#6269
⟨
a
,
b
|
aaa
=
a
,
baabb
=
b
⟩
Next:
#6271
⟨
a
,
b
|
aaa
=
a
,
babab
=
b
⟩
Properties
Presentation has sum-of-sides 10
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
⇒
a
a
2
c
⇒
c
c
a
2
⇒
c
c
3
⇒
a
2
ba
⇒
aca
bc
⇒
a
c
2
ab
⇒
c
cb
⇒
cac
# ab:aaa=a,babab=a ac/b ab=c frequency:2/2 aaa=a aac=c caa=c ccc=aa ba=aca bc=acc ab=c cb=cac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
