#12534 ⟨
a
,
b
|
abab
=
ba
,
abbb
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#12531
⟨
a
,
b
|
abab
=
ab
,
bbbb
=
b
⟩
Next:
#12537
⟨
a
,
b
|
abab
=
ba
,
baaa
=
b
⟩
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
a
b
3
⇒
a
b
4
a
⇒
ba
aba
⇒
ba
b
2
b
a
2
⇒ (
a
b
2
)
2
(
b
2
a
)
2
⇒
a
2
b
a
2
b
2
a
⇒ (
bab
)
2
a
4
⇒
b
3
a
# ab:abab=ba,abbb=a b/a abbb=a bbbba=ba aba=babb baa=abbabb bbabba=aab aabba=babbab aaaa=bbba
Right Cayley graph (truncated)
Left Cayley graph (truncated)
