#12454 ⟨
a
,
b
|
aabb
=
ab
,
abaa
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#12452
⟨
a
,
b
|
aabb
=
aa
,
bbbb
=
a
⟩
Next:
#12457
⟨
a
,
b
|
aabb
=
ab
,
abba
=
a
⟩
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
<
c
<
b
Auxiliary generator:
ab=c
ab
⇒
c
cb
⇒
c
2
aca
⇒
a
a
c
2
⇒
c
c
a
2
⇒
a
cac
⇒
c
# ab:aabb=ab,abaa=a acb ab=c frequency:2/0 ab=c cb=cc aca=a acc=c caa=a cac=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
