WORST_CASE(?,O(n^1))
* Step 1: InnermostRuleRemoval WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
add(0(),X) -> X
add(s(X),Y) -> s(add(X,Y))
dbl(0()) -> 0()
dbl(s(X)) -> s(s(dbl(X)))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
half(0()) -> 0()
half(dbl(X)) -> X
half(s(0())) -> 0()
half(s(s(X))) -> s(half(X))
s(X) -> n__s(X)
sqr(0()) -> 0()
sqr(s(X)) -> s(add(sqr(X),dbl(X)))
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0
,recip/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,add,dbl,first,half,s,sqr
,terms} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
InnermostRuleRemoval
+ Details:
Arguments of following rules are not normal-forms.
add(s(X),Y) -> s(add(X,Y))
dbl(s(X)) -> s(s(dbl(X)))
first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
half(s(0())) -> 0()
half(s(s(X))) -> s(half(X))
sqr(s(X)) -> s(add(sqr(X),dbl(X)))
All above mentioned rules can be savely removed.
* Step 2: DependencyPairs WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
add(0(),X) -> X
dbl(0()) -> 0()
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
half(0()) -> 0()
half(dbl(X)) -> X
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0
,recip/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,add,dbl,first,half,s,sqr
,terms} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
DependencyPairs {dpKind_ = WIDP}
+ Details:
We add the following weak innermost dependency pairs:
Strict DPs
activate#(X) -> c_1()
activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) -> c_3(s#(activate(X)))
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
add#(0(),X) -> c_5()
dbl#(0()) -> c_6()
first#(X1,X2) -> c_7()
first#(0(),X) -> c_8()
half#(0()) -> c_9()
half#(dbl(X)) -> c_10()
s#(X) -> c_11()
sqr#(0()) -> c_12()
terms#(N) -> c_13(sqr#(N))
terms#(X) -> c_14()
Weak DPs
and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
activate#(X) -> c_1()
activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) -> c_3(s#(activate(X)))
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
add#(0(),X) -> c_5()
dbl#(0()) -> c_6()
first#(X1,X2) -> c_7()
first#(0(),X) -> c_8()
half#(0()) -> c_9()
half#(dbl(X)) -> c_10()
s#(X) -> c_11()
sqr#(0()) -> c_12()
terms#(N) -> c_13(sqr#(N))
terms#(X) -> c_14()
- Strict TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
add(0(),X) -> X
dbl(0()) -> 0()
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
half(0()) -> 0()
half(dbl(X)) -> X
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
activate#(X) -> c_1()
activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) -> c_3(s#(activate(X)))
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
add#(0(),X) -> c_5()
dbl#(0()) -> c_6()
first#(X1,X2) -> c_7()
first#(0(),X) -> c_8()
half#(0()) -> c_9()
s#(X) -> c_11()
sqr#(0()) -> c_12()
terms#(N) -> c_13(sqr#(N))
terms#(X) -> c_14()
* Step 4: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict DPs:
activate#(X) -> c_1()
activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) -> c_3(s#(activate(X)))
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
add#(0(),X) -> c_5()
dbl#(0()) -> c_6()
first#(X1,X2) -> c_7()
first#(0(),X) -> c_8()
half#(0()) -> c_9()
s#(X) -> c_11()
sqr#(0()) -> c_12()
terms#(N) -> c_13(sqr#(N))
terms#(X) -> c_14()
- Strict TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs}
+ Details:
The weightgap principle applies using the following constant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
uargs(cons) = {1},
uargs(first) = {1,2},
uargs(recip) = {1},
uargs(s) = {1},
uargs(terms) = {1},
uargs(first#) = {1,2},
uargs(s#) = {1},
uargs(terms#) = {1},
uargs(c_2) = {1},
uargs(c_3) = {1},
uargs(c_4) = {1},
uargs(c_13) = {1}
Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(0) = [0]
p(activate) = [5] x1 + [1]
p(add) = [0]
p(cons) = [1] x1 + [1]
p(dbl) = [0]
p(first) = [1] x1 + [1] x2 + [5]
p(half) = [0]
p(n__first) = [1] x1 + [1] x2 + [4]
p(n__s) = [1] x1 + [1]
p(n__terms) = [1] x1 + [1]
p(nil) = [0]
p(recip) = [1] x1 + [0]
p(s) = [1] x1 + [4]
p(sqr) = [1] x1 + [1]
p(terms) = [1] x1 + [4]
p(activate#) = [5] x1 + [6]
p(add#) = [0]
p(dbl#) = [0]
p(first#) = [1] x1 + [1] x2 + [8]
p(half#) = [0]
p(s#) = [1] x1 + [4]
p(sqr#) = [1] x1 + [13]
p(terms#) = [1] x1 + [9]
p(c_1) = [0]
p(c_2) = [1] x1 + [0]
p(c_3) = [1] x1 + [0]
p(c_4) = [1] x1 + [0]
p(c_5) = [0]
p(c_6) = [0]
p(c_7) = [0]
p(c_8) = [0]
p(c_9) = [0]
p(c_10) = [0]
p(c_11) = [0]
p(c_12) = [0]
p(c_13) = [1] x1 + [0]
p(c_14) = [0]
Following rules are strictly oriented:
activate#(X) = [5] X + [6]
> [0]
= c_1()
activate#(n__first(X1,X2)) = [5] X1 + [5] X2 + [26]
> [5] X1 + [5] X2 + [10]
= c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) = [5] X + [11]
> [5] X + [5]
= c_3(s#(activate(X)))
activate#(n__terms(X)) = [5] X + [11]
> [5] X + [10]
= c_4(terms#(activate(X)))
first#(X1,X2) = [1] X1 + [1] X2 + [8]
> [0]
= c_7()
first#(0(),X) = [1] X + [8]
> [0]
= c_8()
s#(X) = [1] X + [4]
> [0]
= c_11()
sqr#(0()) = [13]
> [0]
= c_12()
terms#(X) = [1] X + [9]
> [0]
= c_14()
activate(X) = [5] X + [1]
> [1] X + [0]
= X
activate(n__first(X1,X2)) = [5] X1 + [5] X2 + [21]
> [5] X1 + [5] X2 + [7]
= first(activate(X1),activate(X2))
activate(n__s(X)) = [5] X + [6]
> [5] X + [5]
= s(activate(X))
activate(n__terms(X)) = [5] X + [6]
> [5] X + [5]
= terms(activate(X))
first(X1,X2) = [1] X1 + [1] X2 + [5]
> [1] X1 + [1] X2 + [4]
= n__first(X1,X2)
first(0(),X) = [1] X + [5]
> [0]
= nil()
s(X) = [1] X + [4]
> [1] X + [1]
= n__s(X)
sqr(0()) = [1]
> [0]
= 0()
terms(N) = [1] N + [4]
> [1] N + [2]
= cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) = [1] X + [4]
> [1] X + [1]
= n__terms(X)
Following rules are (at-least) weakly oriented:
add#(0(),X) = [0]
>= [0]
= c_5()
dbl#(0()) = [0]
>= [0]
= c_6()
half#(0()) = [0]
>= [0]
= c_9()
terms#(N) = [1] N + [9]
>= [1] N + [13]
= c_13(sqr#(N))
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 5: PredecessorEstimation WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
add#(0(),X) -> c_5()
dbl#(0()) -> c_6()
half#(0()) -> c_9()
terms#(N) -> c_13(sqr#(N))
- Weak DPs:
activate#(X) -> c_1()
activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) -> c_3(s#(activate(X)))
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
first#(X1,X2) -> c_7()
first#(0(),X) -> c_8()
s#(X) -> c_11()
sqr#(0()) -> c_12()
terms#(X) -> c_14()
- Weak TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
PredecessorEstimation {onSelection = all simple predecessor estimation selector}
+ Details:
We estimate the number of application of
{1,2,3}
by application of
Pre({1,2,3}) = {}.
Here rules are labelled as follows:
1: add#(0(),X) -> c_5()
2: dbl#(0()) -> c_6()
3: half#(0()) -> c_9()
4: terms#(N) -> c_13(sqr#(N))
5: activate#(X) -> c_1()
6: activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
7: activate#(n__s(X)) -> c_3(s#(activate(X)))
8: activate#(n__terms(X)) -> c_4(terms#(activate(X)))
9: first#(X1,X2) -> c_7()
10: first#(0(),X) -> c_8()
11: s#(X) -> c_11()
12: sqr#(0()) -> c_12()
13: terms#(X) -> c_14()
* Step 6: RemoveWeakSuffixes WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
terms#(N) -> c_13(sqr#(N))
- Weak DPs:
activate#(X) -> c_1()
activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
activate#(n__s(X)) -> c_3(s#(activate(X)))
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
add#(0(),X) -> c_5()
dbl#(0()) -> c_6()
first#(X1,X2) -> c_7()
first#(0(),X) -> c_8()
half#(0()) -> c_9()
s#(X) -> c_11()
sqr#(0()) -> c_12()
terms#(X) -> c_14()
- Weak TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
RemoveWeakSuffixes
+ Details:
Consider the dependency graph
1:S:terms#(N) -> c_13(sqr#(N))
-->_1 sqr#(0()) -> c_12():12
2:W:activate#(X) -> c_1()
3:W:activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
-->_1 first#(0(),X) -> c_8():9
-->_1 first#(X1,X2) -> c_7():8
4:W:activate#(n__s(X)) -> c_3(s#(activate(X)))
-->_1 s#(X) -> c_11():11
5:W:activate#(n__terms(X)) -> c_4(terms#(activate(X)))
-->_1 terms#(X) -> c_14():13
-->_1 terms#(N) -> c_13(sqr#(N)):1
6:W:add#(0(),X) -> c_5()
7:W:dbl#(0()) -> c_6()
8:W:first#(X1,X2) -> c_7()
9:W:first#(0(),X) -> c_8()
10:W:half#(0()) -> c_9()
11:W:s#(X) -> c_11()
12:W:sqr#(0()) -> c_12()
13:W:terms#(X) -> c_14()
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
10: half#(0()) -> c_9()
7: dbl#(0()) -> c_6()
6: add#(0(),X) -> c_5()
13: terms#(X) -> c_14()
4: activate#(n__s(X)) -> c_3(s#(activate(X)))
11: s#(X) -> c_11()
3: activate#(n__first(X1,X2)) -> c_2(first#(activate(X1),activate(X2)))
8: first#(X1,X2) -> c_7()
9: first#(0(),X) -> c_8()
2: activate#(X) -> c_1()
12: sqr#(0()) -> c_12()
* Step 7: SimplifyRHS WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
terms#(N) -> c_13(sqr#(N))
- Weak DPs:
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
- Weak TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
SimplifyRHS
+ Details:
Consider the dependency graph
1:S:terms#(N) -> c_13(sqr#(N))
5:W:activate#(n__terms(X)) -> c_4(terms#(activate(X)))
-->_1 terms#(N) -> c_13(sqr#(N)):1
Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
terms#(N) -> c_13()
* Step 8: Trivial WORST_CASE(?,O(1))
+ Considered Problem:
- Strict DPs:
terms#(N) -> c_13()
- Weak DPs:
activate#(n__terms(X)) -> c_4(terms#(activate(X)))
- Weak TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
Trivial
+ Details:
Consider the dependency graph
1:S:terms#(N) -> c_13()
2:W:activate#(n__terms(X)) -> c_4(terms#(activate(X)))
-->_1 terms#(N) -> c_13():1
The dependency graph contains no loops, we remove all dependency pairs.
* Step 9: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(n__s(X)) -> s(activate(X))
activate(n__terms(X)) -> terms(activate(X))
first(X1,X2) -> n__first(X1,X2)
first(0(),X) -> nil()
s(X) -> n__s(X)
sqr(0()) -> 0()
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
terms(X) -> n__terms(X)
- Signature:
{activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1,activate#/1,add#/2,dbl#/1,first#/2,half#/1,s#/1
,sqr#/1,terms#/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0,recip/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
,c_6/0,c_7/0,c_8/0,c_9/0,c_10/0,c_11/0,c_12/0,c_13/0,c_14/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate#,add#,dbl#,first#,half#,s#,sqr#
,terms#} and constructors {0,cons,n__first,n__s,n__terms,nil,recip}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))