#19498 ⟨
a
,
b
|
aab
=
a
,
bbbba
=
ba
⟩
Up:
Monoid enumeration
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#19494
⟨
a
,
b
|
aab
=
a
,
bbbab
=
ba
⟩
Next:
#19502
⟨
a
,
b
|
aab
=
a
,
bbbbb
=
ba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
3
=
a
and
a
⋅ 1 =
a
, however
a
3
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
3
⋅
a
=
a
and 1 ⋅
a
=
a
, 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(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
⇒
a
[6]
2.
ab
⇒
a
3
[7]
3.
b
4
a
⇒
ba
[2]
# ab:aab=a,bbbba=ba a/b - - aaaa=a ab=aaa bbbba=ba