#25678 ⟨
a
,
b
|
aa
=
a
,
abba
=
abab
⟩
Up:
Monoids with two generators and two relations
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#25659
⟨
a
,
b
|
ab
=
a
,
bbbbb
=
bbb
⟩
Next:
#25684
⟨
a
,
b
|
aa
=
a
,
abbb
=
abab
⟩
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
a
2
⇒
a
ac
⇒
c
ab
⇒
c
c
2
a
⇒
c
2
c
2
b
⇒
c
3
cba
⇒
c
2
cbc
⇒
c
3
# ab:aa=a,abba=abab acb ab=c frequency:2/1 aa=a ac=c ab=c cca=cc ccb=ccc cba=cc cbc=ccc
Right Cayley graph (truncated)
Left Cayley graph (truncated)
