#15544 ⟨
a
,
b
|
aaa
=
bb
,
bbbbb
=
b
⟩
Up:
Monoid enumeration
Prev:
#15543
⟨
a
,
b
|
aaa
=
bb
,
bbbbb
=
a
⟩
Next:
#15565
⟨
a
,
b
|
aab
=
aa
,
ababa
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
2
b
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
a
6
=
b
and
b
⋅ 1 =
b
, however
a
6
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
8
⋅
a
=
a
3
and
a
2
⋅
a
=
a
3
, however
a
8
≠
a
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.
a
9
⇒
a
3
[5]
2.
b
a
6
⇒
b
[4]
3.
a
3
b
⇒
b
a
3
[3]
4.
b
2
⇒
a
3
[1]
# ab:aaa=bb,bbbbb=b a/b - - aaaaaaaaa=aaa baaaaaa=b aaab=baaa bb=aaa