#13223 ⟨
a
,
b
|
baa
=
aab
,
bab
=
ab
⟩
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Monoid enumeration
Prev:
#13221
⟨
a
,
b
|
abb
=
aba
,
bbb
=
bb
⟩
Next:
#13224
⟨
a
,
b
|
baa
=
aab
,
bab
=
bb
⟩
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
a
is not injective:
a
⋅
a
b
2
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however
a
b
2
≠
ab
Not right cancellative, because right multiplication by
b
is not injective:
ba
⋅
b
=
ab
and
a
⋅
b
=
ab
, however
ba
≠
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
2
⇒
a
2
b
[1]
2.
bab
⇒
ab
[2]
3.
a
2
b
2
⇒
a
2
b
[3]
# ab:baa=aab,bab=ab ab - - baa=aab bab=ab aabb=aab