#4191 ⟨
a
,
b
|
aabbbaaab
=
ab
⟩
Up:
Monoid enumeration
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#4190
⟨
a
,
b
|
aabbbaaab
=
aa
⟩
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#4192
⟨
a
,
b
|
aabbbaaab
=
ba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
b
3
a
3
b
=
ab
and
a
⋅
b
=
ab
, however
a
b
3
a
3
b
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
3
a
3
⋅
b
=
ab
and
a
⋅
b
=
ab
, however
a
2
b
3
a
3
≠
a
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
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
b
3
a
2
b
⇒
a
2
b
3
ab
[3]
2.
a
b
3
a
3
b
⇒
a
3
b
3
ab
[5]
3.
a
4
b
3
ab
⇒
ab
[4]
# ab:aabbbaaab=ab ab - - abbbaab=aabbbab abbbaaab=aaabbbab aaaabbbab=ab