#58 ⟨
a
,
b
|
aa
=
a
,
bb
=
b
⟩
Up:
Monoids with two generators and two relations
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#57
⟨
a
,
b
|
aa
=
a
,
bb
=
a
⟩
Next:
#59
⟨
a
,
b
|
aa
=
b
,
ab
=
a
⟩
Properties
Presentation has sum-of-sides 6
Isomorphic to ℕ
(2 = 1)
∗ ℕ
(2 = 1)
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
a
2
⇒
a
b
2
⇒
b
# ab:aa=a,bb=b ab aa=a bb=b
Right Cayley graph (truncated)
Left Cayley graph (truncated)
