#16509 ⟨
a
,
b
|
aab
=
ba
,
abb
=
aaa
⟩
Up:
Monoid enumeration
Prev:
#16506
⟨
a
,
b
|
aab
=
ab
,
bbb
=
aaa
⟩
Next:
#16512
⟨
a
,
b
|
aab
=
ba
,
bab
=
aaa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
2
=
a
3
and
a
⋅
a
2
=
a
3
, however
b
2
≠
a
2
Not right cancellative, because right multiplication by
a
is not injective:
a
4
⋅
a
=
a
4
and
a
3
⋅
a
=
a
4
, however
a
4
≠
a
3
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.
a
5
⇒
a
4
[6]
2.
ba
⇒
a
2
b
[1]
3.
a
b
2
⇒
a
3
[2]
# ab:aab=ba,abb=aaa reversed:a/b - - aaaaa=aaaa ba=aab abb=aaa