#2271 ⟨
a
,
b
|
aabbbaa
=
aba
⟩
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Monoids with two generators and one relation
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#2270
⟨
a
,
b
|
aabbbaa
=
aab
⟩
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#2272
⟨
a
,
b
|
aabbbaa
=
abb
⟩
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
⋅
a
b
3
a
2
=
aba
and
a
⋅
ba
=
aba
, however
a
b
3
a
2
≠
ba
Not right cancellative, because right multiplication by
a
is not injective:
a
2
b
3
a
⋅
a
=
aba
and
ab
⋅
a
=
aba
, however
a
2
b
3
a
≠
ab
Enveloping group: ⟨
a
,
b
|
aaaabb
⟩
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
3
a
2
⇒
aba
[1]
2.
aba
b
3
a
2
⇒
a
2
b
3
aba
[2]
# ab:aabbbaa=aba ab aabbbaa=aba ababbbaa=aabbbaba