#6237 ⟨
a
,
b
|
aba
=
b
,
bbbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#6205
⟨
a
,
b
|
aba
=
b
,
aaaabb
=1⟩
Next:
#6238
⟨
a
,
b
|
aaa
=
a
,
aaaaa
=
a
⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
a
-1
=
ba
b
5
b
-1
=
b
5
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
aba
⇒
b
b
2
a
⇒
a
b
2
b
6
⇒ 1
# ab:aba=b,bbbbbb=1 ab aba=b bba=abb bbbbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
