#474 ⟨
a
,
b
|
ababab
=
ba
⟩
Up:
Monoids with two generators and one relation
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#473
⟨
a
,
b
|
ababab
=
ab
⟩
Next:
#475
⟨
a
,
b
|
ababba
=
aa
⟩
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(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Auxiliary generator:
ba=c
c
3
b
⇒
bc
a
c
2
b
⇒
c
ba
⇒
c
ca
⇒
a
c
3
# ab:ababab=ba bc/a ba=c magic:0 cccb=bc accb=c ba=c ca=accc
Right Cayley graph (truncated)
Left Cayley graph (truncated)
