#479 ⟨
a
,
b
|
abbaab
=
aa
⟩
Up:
Monoids with two generators and one relation
Prev:
#478
⟨
a
,
b
|
ababba
=
bb
⟩
Next:
#480
⟨
a
,
b
|
abbaab
=
ab
⟩
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Auxiliary generator:
bb=c
(
ac
)
2
a
2
c
⇒
a
2
a
(
a
2
c
)
2
⇒ (
ac
)
2
a
3
cb
⇒
bc
a
2
b
⇒
ac
a
2
c
b
2
⇒
c
# ab:abbaab=aa ca/b bb=c frequency:2/3 acacaac=aa aaacaac=acacaaa cb=bc aab=acaac bb=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
