#20189 ⟨
a
,
b
|
aba
=
a
,
aaab
=
bbb
⟩
Up:
Monoids with two generators and two relations
Prev:
#20188
⟨
a
,
b
|
aba
=
a
,
aaab
=
bba
⟩
Next:
#20194
⟨
a
,
b
|
aba
=
a
,
aaba
=
baa
⟩
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
8
⇒
a
3
b
a
3
⇒
a
7
aba
⇒
a
a
3
b
2
⇒
a
7
b
b
3
⇒
a
3
b
# ab:aba=a,aaab=bbb a/b aaaaaaaa=aaa baaa=aaaaaaa aba=a aaabb=aaaaaaab bbb=aaab
Right Cayley graph (truncated)
Left Cayley graph (truncated)
