#5417 ⟨
a
,
b
|
aaaaaa
=
aaaaa
⟩
Up:
Monoid enumeration
Prev:
#5416
⟨
a
,
b
|
abbbbba
=
bbbb
⟩
Next:
#5418
⟨
a
,
b
|
aaaaaa
=
aaaab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Isomorphic to ℕ
(6 = 5)
∗ ℕ
Infinite non-cancellative non-commutative monoid
Element
a
5
b
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
5
=
a
5
and
a
⋅
a
4
=
a
5
, however
a
5
≠
a
4
Not right cancellative, because right multiplication by
a
is not injective:
a
5
⋅
a
=
a
5
and
a
4
⋅
a
=
a
5
, however
a
5
≠
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 shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
6
⇒
a
5
[1]
# ab:aaaaaa=aaaaa ab - - aaaaaa=aaaaa