#570 ⟨
a
,
b
|
abab
=
abaa
⟩
Up:
Monoids with two generators and one relation
Prev:
#569
⟨
a
,
b
|
abab
=
aabb
⟩
Next:
#571
⟨
a
,
b
|
abba
=
aaaa
⟩
Properties
Presentation has sum-of-sides 8
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 shortlex with
a
<
b
<
c
Auxiliary generator:
abaa=c
c
a
2
⇒
abc
cab
⇒
abc
ab
a
2
⇒
c
(
ab
)
2
⇒
c
cb
a
2
⇒
abac
cbab
⇒
abac
# ab:abab=abaa abc abaa=c magic:0 caa=abc cab=abc abaa=c abab=c cbaa=abac cbab=abac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
