#22785 ⟨
a
,
b
|
aaa
=1,
abaab
=
bab
⟩
Up:
Monoids with two generators and two relations
Prev:
#22327
⟨
a
,
b
|
aaa
=1,
bbbbbb
=
bb
⟩
Next:
#22786
⟨
a
,
b
|
aaa
=1,
abaab
=
bba
⟩
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
⇒ 1
a
2
c
2
⇒
cac
(
ac
)
2
⇒
c
2
c
2
ac
⇒
a
c
3
b
⇒
a
2
c
# ab:aaa=1,abaab=bab ac/b ab=c frequency:2/0 aaa=1 aacc=cac acac=cc ccac=accc b=aac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
