#2272 ⟨
a
,
b
|
aabbbaa
=
abb
⟩
Up:
Monoids with two generators and one relation
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#2271
⟨
a
,
b
|
aabbbaa
=
aba
⟩
Next:
#2273
⟨
a
,
b
|
aabbbaa
=
bab
⟩
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:
abb=c
acb
a
2
⇒
c
c
2
b
a
2
⇒
acbac
a
b
2
⇒
c
c
b
2
⇒
acbac
# ab:aabbbaa=abb ac/b abb=c magic:0 acbaa=c ccbaa=acbac abb=c cbb=acbac
Right Cayley graph (truncated)
Left Cayley graph (truncated)
