#1018 ⟨
a
,
b
|
aaaaba
=
aab
⟩
Up:
Monoids with two generators and one relation
Prev:
#1017
⟨
a
,
b
|
aaaaba
=
aaa
⟩
Next:
#1019
⟨
a
,
b
|
aaaaba
=
aba
⟩
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Auxiliary generator:
aab=c
a
2
c
2
⇒ (
ca
)
2
a
2
ca
⇒
c
cb
⇒
c
2
a
cab
⇒ (
ca
)
2
a
2
b
⇒
c
# ab:aaaaba=aab ca/b aab=c magic:0 aacc=caca aaca=c cb=cca cab=caca aab=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
