#1003 ⟨
a
,
b
|
aaaaaa
=
aaa
⟩
Up:
Monoids with two generators and one relation
Prev:
#1002
⟨
a
,
b
|
abbbbba
=
bb
⟩
Next:
#1004
⟨
a
,
b
|
aaaaaa
=
aab
⟩
Properties
Presentation has sum-of-sides 9
Isomorphic to ℕ
(6 = 3)
∗ ℕ
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
6
⇒
a
3
# ab:aaaaaa=aaa ab aaaaaa=aaa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
