#1257 ⟨
a
,
b
|
ababa
=
aaba
⟩
Up:
Monoids with two generators and one relation
Prev:
#1256
⟨
a
,
b
|
ababa
=
aaab
⟩
Next:
#1258
⟨
a
,
b
|
ababa
=
aabb
⟩
Properties
Presentation has sum-of-sides 9
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(
c
) = deg(
a
) = 1,
c
<
a
Auxiliary generator:
aaba=c
cbc
⇒
c
2
ac
⇒
cba
abc
⇒
cba
c
(
ba
)
2
⇒
caba
a
2
ba
⇒
c
a
(
ba
)
2
⇒
c
# ab:ababa=aaba b/ca aaba=c magic:0 cbc=cc ac=cba abc=cba cbaba=caba aaba=c ababa=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
