#2106 ⟨
a
,
b
|
aaaaaba
=
aab
⟩
Up:
Monoids with two generators and one relation
Prev:
#2105
⟨
a
,
b
|
aaaaaba
=
aaa
⟩
Next:
#2107
⟨
a
,
b
|
aaaaaba
=
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Auxiliary generator:
aab=c
a
3
c
2
⇒
c
a
2
ca
a
3
ca
⇒
c
cb
⇒ (
ca
)
2
cab
⇒
c
a
2
ca
a
2
b
⇒
c
# ab:aaaaaba=aab ca/b aab=c magic:0 aaacc=caaca aaaca=c cb=caca cab=caaca aab=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
