#2024 ⟨
a
,
b
|
abaaaaba
=
ab
⟩
Up:
Monoids with two generators and one relation
Prev:
#2023
⟨
a
,
b
|
abaaaaba
=
aa
⟩
Next:
#2025
⟨
a
,
b
|
abaaaaba
=
bb
⟩
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Auxiliary generator:
ab=c
cac
⇒
c
2
a
c
a
2
c
⇒
c
2
a
2
c
a
3
c
⇒
c
2
a
3
c
2
a
4
⇒
c
cb
⇒
c
3
a
3
ab
⇒
c
# ab:abaaaaba=ab ca/b ab=c magic:0 cac=cca caac=ccaa caaac=ccaaa ccaaaa=c cb=cccaaa ab=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
