#2669 ⟨
a
,
b
|
abaab
=
aaaaa
⟩
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Monoid enumeration
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#2668
⟨
a
,
b
|
abaaa
=
aabbb
⟩
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#2670
⟨
a
,
b
|
abaab
=
aaaab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
a
2
b
=
a
5
and
a
⋅
a
4
=
a
5
, however
b
a
2
b
≠
a
4
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.
a
7
b
⇒
ab
a
6
[2]
2.
ab
a
2
b
⇒
a
5
[1]
# ab:abaab=aaaaa a/b - - aaaaaaab=abaaaaaa abaab=aaaaa