#20117 ⟨
a
,
b
|
aab
=
b
,
baaa
=
bab
⟩
Up:
Monoid enumeration
Prev:
#20116
⟨
a
,
b
|
aab
=
b
,
baaa
=
baa
⟩
Next:
#20118
⟨
a
,
b
|
aab
=
b
,
baaa
=
bba
⟩
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
⋅
ab
=
b
a
3
and
b
⋅
a
3
=
b
a
3
, however
ab
≠
a
3
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
9
⇒
b
a
3
[4]
2.
a
2
b
⇒
b
[1]
3.
b
2
⇒
b
a
6
[3]
4.
bab
⇒
b
a
3
[2]
# ab:aab=b,baaa=bab a/b - - baaaaaaaaa=baaa aab=b bb=baaaaaa bab=baaa