#6550 ⟨
a
,
b
|
aaa
=
a
,
abbb
=
ba
⟩
Up:
Monoids with two generators and two relations
Prev:
#6549
⟨
a
,
b
|
aaa
=
a
,
abbb
=
ab
⟩
Next:
#6551
⟨
a
,
b
|
aaa
=
a
,
abbb
=
bb
⟩
Properties
Presentation has sum-of-sides 10
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(
b
) = 0; deg(
a
) = 1
a
b
27
⇒
a
b
3
ba
⇒
a
b
3
a
3
⇒
a
# ab:aaa=a,abbb=ba b/a abbbbbbbbbbbbbbbbbbbbbbbbbbb=abbb ba=abbb aaa=a
Right Cayley graph (truncated)
Left Cayley graph (truncated)
