#2670 ⟨
a
,
b
|
abaab
=
aaaab
⟩
Up:
Monoids with two generators and one relation
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#2669
⟨
a
,
b
|
abaab
=
aaaaa
⟩
Next:
#2671
⟨
a
,
b
|
abaab
=
aaaba
⟩
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
⋅
b
a
2
b
=
a
4
b
and
a
⋅
a
3
b
=
a
4
b
, however
b
a
2
b
≠
a
3
b
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
2
⋅
b
=
a
4
b
and
a
4
⋅
b
=
a
4
b
, however
ab
a
2
≠
a
4
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
Reduction order:
Left-to-right shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
b
⇒
ab
a
2
b
[1]
# ab:abaab=aaaab ba aaaab=abaab