#2498 ⟨
a
,
b
|
aababa
=
aabb
⟩
Up:
Monoids with two generators and one relation
Prev:
#2497
⟨
a
,
b
|
aababa
=
aaba
⟩
Next:
#2499
⟨
a
,
b
|
aababa
=
abaa
⟩
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(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Auxiliary generator:
aabb=c
a
2
b
2
⇒
c
a
2
(
ba
)
2
⇒
c
ca
b
2
⇒
a
(
ab
)
2
c
ca
(
ba
)
2
⇒
a
(
ab
)
2
c
# ab:aababa=aabb ac/b aabb=c magic:0 aabb=c aababa=c cabb=aababc cababa=aababc
Right Cayley graph (truncated)
Left Cayley graph (truncated)
