#14530 ⟨
a
,
b
|
aaab
=
b
,
bbbaa
=
b
⟩
Up:
Monoid enumeration
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#14528
⟨
a
,
b
|
aaab
=
b
,
bbabb
=
b
⟩
Next:
#14532
⟨
a
,
b
|
aaab
=
b
,
bbbab
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
b
6
=
b
and
b
⋅ 1 =
b
, however
b
6
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
a
3
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
3
≠ 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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
7
⇒
b
[7]
2.
bab
⇒
b
4
[3]
3.
b
a
2
⇒
b
5
[8]
4.
a
3
b
⇒
b
[1]
# ab:aaab=b,bbbaa=b b/a - - bbbbbbb=b bab=bbbb baa=bbbbb aaab=b