#5682 ⟨
a
,
b
|
aababa
=
aabab
⟩
Up:
Monoids with two generators and one relation
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#5681
⟨
a
,
b
|
aababa
=
aabaa
⟩
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#5683
⟨
a
,
b
|
aababa
=
aabba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
(
ba
)
2
=
a
(
ab
)
2
and
a
⋅ (
ab
)
2
=
a
(
ab
)
2
, however
a
(
ba
)
2
≠ (
ab
)
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
=
aabab
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
c
[4]
2.
cbab
⇒
c
2
[5]
3.
a
(
ab
)
2
⇒
c
[2]
# ab:aababa=aabab abc aabab=c magic:0 ca=c cbab=cc aabab=c