#13137 ⟨
a
,
b
|
aab
=
aaa
,
bba
=
ab
⟩
Up:
Monoid enumeration
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#13136
⟨
a
,
b
|
aab
=
aaa
,
bba
=
aa
⟩
Next:
#13138
⟨
a
,
b
|
aab
=
aaa
,
bba
=
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
b
is not injective:
b
⋅
b
11
a
2
=
b
8
a
2
and
b
⋅
b
7
a
2
=
b
8
a
2
, however
b
11
a
2
≠
b
7
a
2
Not right cancellative, because right multiplication by
a
is not injective:
a
2
⋅
a
=
b
4
a
2
and
b
4
a
⋅
a
=
b
4
a
2
, however
a
2
≠
b
4
a
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
b
2
a
[2]
2.
b
12
a
2
⇒
b
8
a
2
[4]
3.
a
3
⇒
b
4
a
2
[3]
# ab:aab=aaa,bba=ab reversed:b/a - - ab=bba bbbbbbbbbbbbaa=bbbbbbbbaa aaa=bbbbaa