#19824 ⟨
a
,
b
|
aaa
=
a
,
abbb
=
baa
⟩
Up:
Monoids with two generators and two relations
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#19823
⟨
a
,
b
|
aaa
=
a
,
abbb
=
abb
⟩
Next:
#19825
⟨
a
,
b
|
aaa
=
a
,
abbb
=
bab
⟩
Properties
Presentation has sum-of-sides 11
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
a
2
ba
⇒
ba
a
b
3
⇒
b
a
2
(
ba
)
2
⇒
a
b
2
a
b
3
a
⇒
aba
a
2
b
2
a
⇒
b
2
a
ba
b
2
a
⇒
ba
# ab:aaa=a,abbb=baa ab aaa=a aaba=ba abbb=baa baba=abba bbba=aba aabba=bba babba=ba
Right Cayley graph (truncated)
Left Cayley graph (truncated)
