#1338 ⟨
a
,
b
|
aaabaaaaba
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#1336
⟨
a
,
b
|
aaaabbbbba
=1⟩
Next:
#1339
⟨
a
,
b
|
aaabaaaabb
=1⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Group inverses:
a
-1
=
a
3
b
a
4
b
b
-1
=
a
4
b
a
4
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
b
a
4
ba
⇒
ab
a
4
b
(
a
4
b
)
2
⇒ 1
# ab:aaabaaaaba=1 ab baaaaba=abaaaab aaaabaaaab=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
1394
⟨
a
,
b
|
aabaaaabaa
=1⟩
φ
(
a
) =
a
,
φ
(
b
) =
b