#16533 ⟨
a
,
b
|
aba
=
aa
,
bbb
=
aba
⟩
Up:
Monoids with two generators and two relations
Prev:
#16532
⟨
a
,
b
|
aba
=
aa
,
bbb
=
aaa
⟩
Next:
#16534
⟨
a
,
b
|
aba
=
ab
,
abb
=
aaa
⟩
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
aba
⇒
a
2
b
a
2
⇒
a
2
b
b
3
⇒
a
2
a
3
b
⇒
a
3
a
5
⇒
a
3
a
2
b
2
a
⇒
a
3
# ab:aba=aa,bbb=aba ab aba=aa baa=aab bbb=aa aaab=aaa aaaaa=aaa aabba=aaa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
