#259 ⟨
a
,
b
|
abab
=
aaa
⟩
Up:
Monoids with two generators and one relation
Prev:
#258
⟨
a
,
b
|
aabb
=
baa
⟩
Next:
#260
⟨
a
,
b
|
abab
=
aab
⟩
Properties
Presentation has sum-of-sides 7
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
b
<
a
(
ab
)
2
⇒
a
3
a
4
b
⇒
ab
a
3
# ab:abab=aaa ba abab=aaa aaaab=abaaa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
