#13036 ⟨
a
,
b
|
abb
=
aba
,
bbaa
=
a
⟩
Up:
Monoid enumeration
Prev:
#13029
⟨
a
,
b
|
abb
=
aba
,
baaa
=
b
⟩
Next:
#13040
⟨
a
,
b
|
abb
=
aba
,
bbba
=
a
⟩
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
⋅
b
2
=
aba
and
a
⋅
ba
=
aba
, however
b
2
≠
ba
Not right cancellative, because right multiplication by
a
is not injective:
b
2
a
⋅
a
=
a
and 1 ⋅
a
=
a
, however
b
2
a
≠ 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
b
2
⇒
aba
[1]
2.
b
2
a
2
⇒
a
[2]
3.
ab
a
3
⇒
a
2
[3]
4.
(
ab
)
2
a
2
⇒
aba
[4]
# ab:abb=aba,bbaa=a ab - - abb=aba bbaa=a abaaa=aa ababaa=aba