#1689 ⟨
a
,
b
|
abb
=
ab
,
bbb
=
b
⟩
Up:
Monoid enumeration
Prev:
#1687
⟨
a
,
b
|
abb
=
aa
,
bbb
=
b
⟩
Next:
#1691
⟨
a
,
b
|
abb
=
ba
,
bbb
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
b
2
=
b
and
b
⋅ 1 =
b
, however
b
2
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
b
2
⋅
b
=
b
and 1 ⋅
b
=
b
, however
b
2
≠ 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
b
2
⇒
ab
[1]
2.
b
3
⇒
b
[2]
# ab:abb=ab,bbb=b ab - - abb=ab bbb=b