#5051 ⟨
a
,
b
|
aaababa
=
bbba
⟩
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Monoid enumeration
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#5050
⟨
a
,
b
|
aaababa
=
bbab
⟩
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#5052
⟨
a
,
b
|
aaababa
=
bbbb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
a
3
bab
⋅
a
=
b
3
a
and
b
3
⋅
a
=
b
3
a
, however
a
3
bab
≠
b
3
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
3
a
⇒
a
3
(
ba
)
2
[1]
# ab:aaababa=bbba a/b - - bbba=aaababa