#3752 ⟨
a
,
b
|
aaaa
=
aa
,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#3679
⟨
a
,
b
|
aa
=1,
bbbb
=
bbb
⟩
Next:
#3767
⟨
a
,
b
|
aaaa
=
ab
,
bbbb
=1⟩
Properties
Presentation has sum-of-sides 10
Isomorphic to ℤ
4
∗ ℕ
(4 = 2)
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
2
b
4
⇒ 1
# ab:aaaa=aa,bbbb=1 ab aaaa=aa bbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
