#12343 ⟨
a
,
b
|
aaba
=
aa
,
babb
=
b
⟩
Up:
Monoid enumeration
Prev:
#12342
⟨
a
,
b
|
aaba
=
aa
,
babb
=
a
⟩
Next:
#12347
⟨
a
,
b
|
aaba
=
aa
,
bbab
=
b
⟩
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
⋅
a
b
2
=
b
and
b
⋅ 1 =
b
, however
a
b
2
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
bab
⋅
b
=
b
and 1 ⋅
b
=
b
, however
bab
≠ 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 shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
ba
⇒
a
2
[1]
2.
a
2
b
2
⇒
a
2
b
[3]
3.
ba
b
2
⇒
b
[2]
# ab:aaba=aa,babb=b ab - - aaba=aa aabb=aab babb=b