#2122 ⟨
a
,
b
|
aaaabaa
=
aab
⟩
Up:
Monoids with two generators and one relation
Prev:
#2121
⟨
a
,
b
|
aaaabaa
=
aaa
⟩
Next:
#2123
⟨
a
,
b
|
aaaabaa
=
aba
⟩
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(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Auxiliary generator:
aab=c
c
2
a
2
⇒
a
2
c
2
a
2
c
a
2
⇒
c
cac
a
2
⇒
a
(
ac
)
2
cb
⇒
a
2
c
2
a
2
b
⇒
c
cab
⇒
a
(
ac
)
2
# ab:aaaabaa=aab ac/b aab=c magic:0 ccaa=aacc aacaa=c cacaa=aacac cb=aacc aab=c cab=aacac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
