#113 ⟨
a
,
b
|
aaa
=
a
,
bbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#95
⟨
a
,
b
|
aa
=1,
bbb
=
b
⟩
Next:
#116
⟨
a
,
b
|
aaa
=
b
,
abb
=1⟩
Properties
Presentation has sum-of-sides 7
Isomorphic to ℤ
3
∗ 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
⇒ 1
# ab:aaa=a,bbb=1 ab aaa=a bbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
