#2703 ⟨
a
,
b
|
abbab
=
aaaaa
⟩
Up:
Monoid enumeration
Prev:
#2702
⟨
a
,
b
|
abbaa
=
ababb
⟩
Next:
#2704
⟨
a
,
b
|
abbab
=
aaaab
⟩
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
ab
=
a
5
and
a
⋅
a
4
=
a
5
, however
b
2
ab
≠
a
4
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.
a
5
bab
⇒
a
b
2
a
5
[2]
2.
a
b
2
ab
⇒
a
5
[1]
# ab:abbab=aaaaa a/b - - aaaaabab=abbaaaaa abbab=aaaaa