#5820 ⟨
a
,
b
|
abaaab
=
ababb
⟩
Up:
Monoid enumeration
Prev:
#5819
⟨
a
,
b
|
abaaab
=
ababa
⟩
Next:
#5821
⟨
a
,
b
|
abaaab
=
abbaa
⟩
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
a
3
b
=
aba
b
2
and
a
⋅
ba
b
2
=
aba
b
2
, however
b
a
3
b
≠
ba
b
2
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
3
⋅
b
=
aba
b
2
and (
ab
)
2
⋅
b
=
aba
b
2
, however
ab
a
3
≠ (
ab
)
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
b
2
⇒
ab
a
3
b
[1]
# ab:abaaab=ababb a/b - - ababb=abaaab