#5553 ⟨
a
,
b
|
aaabaa
=
babaa
⟩
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Monoids with two generators and one relation
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#5552
⟨
a
,
b
|
aaabaa
=
baabb
⟩
Next:
#5554
⟨
a
,
b
|
aaabaa
=
babab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
a
is not injective:
a
3
ba
⋅
a
=
bab
a
2
and (
ba
)
2
⋅
a
=
bab
a
2
, however
a
3
ba
≠ (
ba
)
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.
bab
a
2
⇒
a
3
b
a
2
[1]
# ab:aaabaa=babaa a/b babaa=aaabaa