#157 ⟨
a
,
b
|
ab
=
aa
,
ba
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#151
⟨
a
,
b
|
ba
=
ab
,
aaa
=1⟩
Next:
#158
⟨
a
,
b
|
ab
=
aa
,
ba
=
b
⟩
Properties
Presentation has sum-of-sides 7
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
<
b
ab
⇒
a
2
ba
⇒
a
a
3
⇒
a
2
# ab:ab=aa,ba=a ab ab=aa ba=a aaa=aa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
