#13225 ⟨
a
,
b
|
baa
=
aab
,
bba
=
aa
⟩
Up:
Monoid enumeration
Prev:
#13224
⟨
a
,
b
|
baa
=
aab
,
bab
=
bb
⟩
Next:
#13226
⟨
a
,
b
|
baa
=
aab
,
bba
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
a
is not injective:
b
2
⋅
a
=
a
2
and
a
⋅
a
=
a
2
, however
b
2
≠
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:
Left-to-right shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
a
⇒
a
2
[2]
2.
a
2
b
⇒
b
a
2
[1]
3.
ab
a
2
⇒
b
a
3
[3]
# ab:baa=aab,bba=aa ba - - bba=aa aab=baa abaa=baaa