#5678 ⟨
a
,
b
|
aababa
=
aaaab
⟩
Up:
Monoid enumeration
Prev:
#5677
⟨
a
,
b
|
aababa
=
aaaaa
⟩
Next:
#5679
⟨
a
,
b
|
aababa
=
aaaba
⟩
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
(
ba
)
2
=
a
4
b
and
a
⋅
a
3
b
=
a
4
b
, however
a
(
ba
)
2
≠
a
3
b
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:
Right-to-left recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
b
⇒
a
2
(
ba
)
2
[1]
# ab:aababa=aaaab reversed:b/a - - aaaab=aababa