#1023 ⟨
a
,
b
|
aaaaba
=
bba
⟩
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Monoid enumeration
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#1022
⟨
a
,
b
|
aaaaba
=
bab
⟩
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#1024
⟨
a
,
b
|
aaaaba
=
bbb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
a
4
b
⋅
a
=
b
2
a
and
b
2
⋅
a
=
b
2
a
, however
a
4
b
≠
b
2
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
2
a
⇒
a
4
ba
[1]
# ab:aaaaba=bba a/b - - bba=aaaaba