#899 ⟨
a
,
b
|
aaabaaa
=
ab
⟩
Up:
Monoids with two generators and one relation
Prev:
#898
⟨
a
,
b
|
aaabaaa
=
aa
⟩
Next:
#900
⟨
a
,
b
|
aaabaaa
=
bb
⟩
Properties
Presentation has sum-of-sides 9
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
c
2
a
3
⇒
a
(
ac
)
2
a
2
c
a
3
⇒
c
cac
a
3
⇒ (
a
2
c
)
2
ab
⇒
c
cb
⇒ (
a
2
c
)
2
# ab:aaabaaa=ab ac/b ab=c magic:0 ccaaa=aacac aacaaa=c cacaaa=aacaac ab=c cb=aacaac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
