#112 ⟨
a
,
b
|
abba
=
ab
⟩
Up:
Monoids with two generators and one relation
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#111
⟨
a
,
b
|
abba
=
aa
⟩
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#113
⟨
a
,
b
|
abba
=
bb
⟩
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
c
<
b
<
a
Auxiliary generator:
abb=c
cb
⇒
c
2
ab
⇒
ca
c
2
a
⇒
c
# ab:abba=ab cba abb=c frequency:3/0 cb=cc ab=ca cca=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
