#429 ⟨
a
,
b
|
aaabaa
=
ab
⟩
Up:
Monoids with two generators and one relation
Prev:
#428
⟨
a
,
b
|
aaabaa
=
aa
⟩
Next:
#430
⟨
a
,
b
|
aaabaa
=
ba
⟩
Properties
Presentation has sum-of-sides 8
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:
ab=c
c
2
a
2
⇒
a
2
c
2
a
2
c
a
2
⇒
c
cac
a
2
⇒
a
(
ac
)
2
ab
⇒
c
cb
⇒
a
(
ac
)
2
# ab:aaabaa=ab ac/b ab=c magic:0 ccaa=aacc aacaa=c cacaa=aacac ab=c cb=aacac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
