#5654 ⟨
a
,
b
|
aabaab
=
abaab
⟩
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Monoid enumeration
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#5653
⟨
a
,
b
|
aabaab
=
abaaa
⟩
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#5655
⟨
a
,
b
|
aabaab
=
ababa
⟩
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
⋅
ab
a
2
b
=
ab
a
2
b
and
a
⋅
b
a
2
b
=
ab
a
2
b
, however
ab
a
2
b
≠
b
a
2
b
Not right cancellative, because right multiplication by
c
is not injective:
a
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
≠ 1
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
Auxiliary generators:
c
=
abaab
Reduction order:
Left-to-right recursive path with deg(
a
) = 0; deg(
c
) = deg(
b
) = 1,
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
c
[4]
2.
abc
⇒
c
a
2
b
[5]
3.
ab
a
2
b
⇒
c
[2]
# ab:aabaab=abaab a/cb abaab=c magic:0 ac=c abc=caab abaab=c