#69 ⟨
a
,
b
|
abaaba
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#67
⟨
a
,
b
|
aabbba
=1⟩
Next:
#70
⟨
a
,
b
|
ababab
=1⟩
Properties
Presentation has sum-of-sides 6
Infinite non-Abelian group
Group inverses:
a
-1
=
ab
a
2
b
b
-1
=
a
2
b
a
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
ba
⇒
ab
a
2
b
(
a
2
b
)
2
⇒ 1
# ab:abaaba=1 ab baaba=abaab aabaab=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
