#12585 ⟨
a
,
b
|
abba
=
ab
,
bbbb
=
b
⟩
Up:
Monoids with two generators and two relations
Prev:
#12582
⟨
a
,
b
|
abba
=
ab
,
bbba
=
a
⟩
Next:
#12591
⟨
a
,
b
|
abba
=
ba
,
bbaa
=
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
b
4
⇒
b
aba
⇒
a
b
3
a
b
2
a
⇒
ab
a
b
3
a
⇒
a
b
2
# ab:abba=ab,bbbb=b b/a bbbb=b aba=abbb abba=ab abbba=abb
Right Cayley graph (truncated)
Left Cayley graph (truncated)
