#500 ⟨
a
,
b
|
aaa
=
a
,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#489
⟨
a
,
b
|
abab
=1,
baba
=1⟩
Next:
#507
⟨
a
,
b
|
aaa
=
b
,
abbb
=1⟩
Properties
Presentation has sum-of-sides 8
Isomorphic to ℕ
(3 = 1)
∗ ℤ
4
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
4
⇒ 1
# ab:aaa=a,bbbb=1 ab aaa=a bbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
Σ
#
Presentation
Mapping
10
3804
⟨
a
,
b
|
aaab
=
ab
,
bbbb
=1⟩
φ
(
a
) =
a
,
φ
(
b
) =
b
