#2550 ⟨
a
,
b
|
aabbba
=
aabb
⟩
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Monoids with two generators and one relation
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#2549
⟨
a
,
b
|
aabbba
=
aaba
⟩
Next:
#2551
⟨
a
,
b
|
aabbba
=
abaa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
b
3
a
=
a
2
b
2
and
a
⋅
a
b
2
=
a
2
b
2
, however
a
b
3
a
≠
a
b
2
Enveloping group is isomorphic to ℤ
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
Auxiliary generators:
c
=
aabb
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
cba
⇒
c
[4]
2.
a
2
b
2
⇒
c
[2]
3.
ca
b
2
⇒
cbc
[5]
# ab:aabbba=aabb abc aabb=c magic:0 cba=c aabb=c cabb=cbc