#26711 ⟨
a
,
b
|
aa
=1,
bbbbbbbb
=
b
⟩
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Monoid enumeration
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#26705
⟨
a
,
b
|
aa
=1,
bbabbbbb
=
b
⟩
Next:
#27079
⟨
a
,
b
|
aa
=1,
aabbbba
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Isomorphic to ℤ
2
∗ ℕ
(8 = 1)
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
b
7
=
b
and
b
⋅ 1 =
b
, however
b
7
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
b
7
⋅
b
=
b
and 1 ⋅
b
=
b
, however
b
7
≠ 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
Reduction order:
Left-to-right shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
b
8
⇒
b
[2]
# ab:aa=1,bbbbbbbb=b ab - - aa=1 bbbbbbbb=b