#15960 ⟨
a
,
b
|
aaa
=
aa
,
abab
=
aa
⟩
Up:
Monoid enumeration
Prev:
#15958
⟨
a
,
b
|
aaa
=
aa
,
aabb
=
ba
⟩
Next:
#15961
⟨
a
,
b
|
aaa
=
aa
,
abab
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
b
2
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
2
=
a
2
and
a
⋅
a
=
a
2
, however
a
2
≠
a
Not right cancellative, because right multiplication by
a
is not injective:
a
2
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
a
2
≠
a
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
3
⇒
a
2
[1]
2.
a
2
b
⇒
ab
a
2
[3]
3.
(
ab
)
2
⇒
a
2
[2]
# ab:aaa=aa,abab=aa a/b - - aaa=aa aab=abaa abab=aa