#1119 ⟨
a
,
b
|
ababab
=
aba
⟩
Up:
Monoids with two generators and one relation
Prev:
#1118
⟨
a
,
b
|
ababab
=
aab
⟩
Next:
#1120
⟨
a
,
b
|
ababab
=
baa
⟩
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(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Auxiliary generator:
aba=c
c
2
b
⇒
cbc
cbc
b
2
⇒
c
(
cb
)
3
⇒
c
2
abc
⇒ (
cb
)
2
ca
⇒
cbc
cba
⇒ (
cb
)
2
aba
⇒
c
# ab:ababab=aba bc/a aba=c magic:0 ccb=cbc cbcbb=c cbcbcb=cc abc=cbcb ca=cbc cba=cbcb aba=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
