#20318 ⟨
a
,
b
|
aba
=
b
,
bbbb
=
bab
⟩
Up:
Monoids with two generators and two relations
Prev:
#20317
⟨
a
,
b
|
aba
=
b
,
bbbb
=
abb
⟩
Next:
#20448
⟨
a
,
b
|
ba
=
ab
,
aaaaaaa
=1⟩
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(
b
) = 0; deg(
a
) = 1
b
6
⇒
b
2
a
b
2
⇒
b
4
bab
⇒
b
4
b
2
a
⇒
b
4
aba
⇒
b
# ab:aba=b,bbbb=bab b/a bbbbbb=bb abb=bbbb bab=bbbb bba=bbbb aba=b
Right Cayley graph (truncated)
Left Cayley graph (truncated)
