#6543 ⟨
a
,
b
|
aaa
=
a
,
abab
=
ba
⟩
Up:
Monoids with two generators and two relations
Prev:
#6542
⟨
a
,
b
|
aaa
=
a
,
abab
=
ab
⟩
Next:
#6544
⟨
a
,
b
|
aaa
=
a
,
abab
=
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:
Right-to-left recursive path with deg(
a
) = 0; deg(
b
) = 1
a
3
⇒
a
a
2
ba
⇒
ba
bab
⇒
aba
b
2
a
⇒
ab
a
2
b
b
a
2
b
2
⇒
b
a
2
# ab:aaa=a,abab=ba reversed:a/b aaa=a aaba=ba bab=aba bba=abaab baabb=baa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
