#123 ⟨
a
,
b
|
bab
=
aba
⟩
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Monoids with two generators and one relation
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#122
⟨
a
,
b
|
bab
=
aaa
⟩
Next:
#124
⟨
a
,
b
|
bbb
=
aaa
⟩
Properties
Presentation has sum-of-sides 6
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 shortlex with
a
<
b
<
c
Auxiliary generator:
aba=c
ca
⇒
bc
cb
⇒
ac
aba
⇒
c
bab
⇒
c
# ab:bab=aba abc aba=c magic:0 ca=bc cb=ac aba=c bab=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
