#5440 ⟨
a
,
b
|
aaaa
=1,
ababab
=1⟩
Up:
Monoids with two generators and two relations
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#5436
⟨
a
,
b
|
aaaa
=1,
aabbbb
=1⟩
Next:
#5442
⟨
a
,
b
|
aaaa
=1,
ababbb
=1⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
3
b
-1
=
a
(
ba
)
2
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
⇒ 1
b
(
ab
)
2
⇒
a
3
# ab:aaaa=1,ababab=1 ab aaaa=1 babab=aaa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
