#1835 ⟨
a
,
b
|
aaaaabaa
=
ab
⟩
Up:
Monoids with two generators and one relation
Prev:
#1834
⟨
a
,
b
|
aaaaabaa
=
aa
⟩
Next:
#1836
⟨
a
,
b
|
aaaaabaa
=
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Auxiliary generator:
ab=c
a
4
c
2
⇒ (
c
a
2
)
2
a
4
cac
⇒
c
a
3
c
a
2
a
4
c
a
2
⇒
c
cb
⇒
c
a
3
c
a
2
ab
⇒
c
# ab:aaaaabaa=ab ca/b ab=c magic:0 aaaacc=caacaa aaaacac=caaacaa aaaacaa=c cb=caaacaa ab=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
