#21786 ⟨
a
,
b
|
aaa
=1,
bbabbbb
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#21783
⟨
a
,
b
|
aaa
=1,
bbaabbb
=
b
⟩
Next:
#21787
⟨
a
,
b
|
aaa
=1,
bbabbbb
=
b
⟩
Properties
Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
2
b
-1
=
b
17
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:
Right-to-left recursive path with deg(
b
) = 0; deg(
a
) = 1
b
18
⇒ 1
a
b
2
⇒
b
8
a
a
3
⇒ 1
# ab:aaa=1,bbabbbb=a reversed:b/a bbbbbbbbbbbbbbbbbb=1 abb=bbbbbbbba aaa=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
