#6534 ⟨
a
,
b
|
aaa
=
a
,
aaba
=
ab
⟩
Up:
Monoids with two generators and two relations
Prev:
#6525
⟨
a
,
b
|
aba
=
b
,
bbbbb
=
b
⟩
Next:
#6535
⟨
a
,
b
|
aaa
=
a
,
aaba
=
ba
⟩
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
ca
⇒
ac
a
3
⇒
a
a
2
c
⇒
c
ab
⇒
c
cb
⇒
a
c
2
# ab:aaa=a,aaba=ab ac/b ab=c frequency:2/0 ca=ac aaa=a aac=c ab=c cb=acc
Right Cayley graph (truncated)
Left Cayley graph (truncated)
