#20233 ⟨
a
,
b
|
aba
=
a
,
baab
=
bbb
⟩
Up:
Monoids with two generators and two relations
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#20231
⟨
a
,
b
|
aba
=
a
,
baab
=
abb
⟩
Next:
#20234
⟨
a
,
b
|
aba
=
a
,
babb
=
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 recursive path with deg(
b
) = 0; deg(
a
) = 1
ba
b
3
⇒
b
3
b
3
ab
⇒
b
3
a
2
b
⇒
a
b
3
aba
⇒
a
a
b
3
a
⇒
a
2
b
a
2
⇒
b
3
a
a
3
⇒
a
b
5
a
# ab:aba=a,baab=bbb b/a babbb=bbb bbbab=bbb aab=abbb aba=a abbba=aa baa=bbba aaa=abbbbba
Right Cayley graph (truncated)
Left Cayley graph (truncated)
