#572 ⟨
a
,
b
|
aaa
=
a
,
bbb
=
b
⟩
Up:
Monoids with two generators and two relations
Prev:
#571
⟨
a
,
b
|
aaa
=
a
,
bbb
=
a
⟩
Next:
#574
⟨
a
,
b
|
aaa
=
b
,
aab
=
b
⟩
Properties
Presentation has sum-of-sides 8
Isomorphic to ℕ
(3 = 1)
∗ ℕ
(3 = 1)
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
a
3
⇒
a
b
3
⇒
b
# ab:aaa=a,bbb=b ab aaa=a bbb=b
Right Cayley graph (truncated)
Left Cayley graph (truncated)
