#3776 ⟨
a
,
b
|
aaaa
=
bb
,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#3773
⟨
a
,
b
|
aaaa
=
bb
,
abbb
=1⟩
Next:
#3780
⟨
a
,
b
|
aaab
=
aa
,
abab
=1⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
3
b
2
b
-1
=
b
3
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
2
a
⇒
a
b
2
a
4
⇒
b
2
b
4
⇒ 1
# ab:aaaa=bb,bbbb=1 ab bba=abb aaaa=bb bbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
