#2488 ⟨
a
,
b
|
aabaab
=
baab
⟩
Up:
Monoids with two generators and one relation
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#2487
⟨
a
,
b
|
aabaab
=
baaa
⟩
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#2489
⟨
a
,
b
|
aabaab
=
baba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
a
2
⋅
b
=
b
a
2
b
and
b
a
2
⋅
b
=
b
a
2
b
, however
a
2
b
a
2
≠
b
a
2
Enveloping group is isomorphic to ℤ
2
∗ 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
=
baab
Reduction order:
Left-to-right recursive path with deg(
a
) = 0; deg(
c
) = deg(
b
) = 1,
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
c
⇒
c
[4]
2.
bc
⇒
c
a
2
b
[5]
3.
b
a
2
b
⇒
c
[2]
# ab:aabaab=baab a/cb baab=c magic:0 aac=c bc=caab baab=c