#15499 ⟨
a
,
b
|
aaa
=
ab
,
bbbab
=
a
⟩
Up:
Monoid enumeration
Prev:
#15497
⟨
a
,
b
|
aaa
=
ab
,
bbbaa
=
a
⟩
Next:
#15501
⟨
a
,
b
|
aaa
=
ab
,
bbbba
=
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
⋅
b
=
a
3
and
a
⋅
a
2
=
a
3
, however
b
≠
a
2
Not right cancellative, because right multiplication by
a
is not injective:
a
8
⋅
a
=
a
and 1 ⋅
a
=
a
, however
a
8
≠ 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
9
⇒
a
[5]
2.
ab
⇒
a
3
[1]
3.
b
3
a
⇒
a
7
[6]
# ab:aaa=ab,bbbab=a a/b - - aaaaaaaaa=a ab=aaa bbba=aaaaaaa