#2702 ⟨
a
,
b
|
abbaa
=
ababb
⟩
Up:
Monoid enumeration
Prev:
#2701
⟨
a
,
b
|
abbaa
=
abaab
⟩
Next:
#2703
⟨
a
,
b
|
abbab
=
aaaaa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
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
a
2
=
aba
b
2
and
a
⋅
ba
b
2
=
aba
b
2
, however
b
2
a
2
≠
ba
b
2
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.
aba
b
2
⇒
a
b
2
a
2
[1]
# ab:abbaa=ababb ba - - ababb=abbaa