#14601 ⟨
a
,
b
|
aaba
=
b
,
aaaaa
=
a
⟩
Up:
Monoid enumeration
Prev:
#14600
⟨
a
,
b
|
aaba
=
a
,
bbbbb
=
b
⟩
Next:
#14631
⟨
a
,
b
|
aaba
=
b
,
abbbb
=
a
⟩
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
4
=
a
and
a
⋅ 1 =
a
, however
a
4
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
4
⋅
a
=
a
and 1 ⋅
a
=
a
, however
a
4
≠ 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:
Right-to-left recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
5
⇒
a
[2]
2.
a
4
b
⇒
b
[7]
3.
ba
⇒
a
2
b
[6]
# ab:aaba=b,aaaaa=a reversed:a/b - - aaaaa=a aaaab=b ba=aab