#20158 ⟨
a
,
b
|
aab
=
b
,
bbab
=
bba
⟩
Up:
Monoids with two generators and two relations
Prev:
#20157
⟨
a
,
b
|
aab
=
b
,
bbab
=
bab
⟩
Next:
#20159
⟨
a
,
b
|
aab
=
b
,
bbab
=
bbb
⟩
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(
a
) = 0; deg(
b
) = 1
a
2
b
⇒
b
b
2
a
3
⇒
b
2
a
b
3
⇒
b
2
a
2
b
2
ab
⇒
b
2
a
# ab:aab=b,bbab=bba a/b aab=b bbaaa=bba bbb=bbaa bbab=bba
Right Cayley graph (truncated)
Left Cayley graph (truncated)
