#704 ⟨
a
,
b
|
abaabaaba
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#701
⟨
a
,
b
|
abaaabbab
=1⟩
Next:
#706
⟨
a
,
b
|
abaababba
=1⟩
Properties
Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
a
-1
=
ab
(
a
2
b
)
2
b
-1
=
a
2
(
b
a
2
)
2
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
b
(
a
2
b
)
2
a
⇒
ab
(
a
2
b
)
2
(
a
2
b
)
3
⇒ 1
# ab:abaabaaba=1 ab baabaaba=abaabaab aabaabaab=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
