#251 ⟨
a
,
b
|
aaba
=
baa
⟩
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Monoid enumeration
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#250
⟨
a
,
b
|
aaba
=
abb
⟩
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#252
⟨
a
,
b
|
aaba
=
bab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
a
2
b
⋅
a
=
b
a
2
and
ba
⋅
a
=
b
a
2
, however
a
2
b
≠
ba
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:
Right-to-left recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
2
⇒
a
2
ba
[1]
# ab:aaba=baa reversed:a/b - - baa=aaba