#1322 ⟨
a
,
b
|
aaaa
=
a
,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#1307
⟨
a
,
b
|
bab
=
aaa
,
bbb
=1⟩
Next:
#1328
⟨
a
,
b
|
aaaa
=
b
,
abbb
=1⟩
Properties
Presentation has sum-of-sides 9
Isomorphic to ℤ
4
∗ ℕ
(4 = 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
4
⇒
a
b
4
⇒ 1
# ab:aaaa=a,bbbb=1 ab aaaa=a bbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
