#2570 ⟨
a
,
b
|
abaaab
=
abbb
⟩
Up:
Monoids with two generators and one relation
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#2569
⟨
a
,
b
|
abaaab
=
abba
⟩
Next:
#2571
⟨
a
,
b
|
abaaab
=
baaa
⟩
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
3
b
=
a
b
3
and
a
⋅
b
3
=
a
b
3
, however
b
a
3
b
≠
b
3
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
3
⋅
b
=
a
b
3
and
a
b
2
⋅
b
=
a
b
3
, however
ab
a
3
≠
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
Reduction order:
Left-to-right recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
3
⇒
ab
a
3
b
[1]
# ab:abaaab=abbb a/b abbb=abaaab