MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            10() -> double(s(double(s(s(0())))))
            1024() -> 1024_1(0())
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10,1024,1024_1,double,if,lt} and constructors {0,false,s
            ,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
          1024#() -> c_2(1024_1#(0()))
          1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
          double#(0()) -> c_4()
          double#(s(x)) -> c_5(double#(x))
          if#(false(),x) -> c_6()
          if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
          lt#(x,0()) -> c_8()
          lt#(0(),s(y)) -> c_9()
          lt#(s(x),s(y)) -> c_10(lt#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            1024#() -> c_2(1024_1#(0()))
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            double#(0()) -> c_4()
            double#(s(x)) -> c_5(double#(x))
            if#(false(),x) -> c_6()
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(x,0()) -> c_8()
            lt#(0(),s(y)) -> c_9()
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024() -> 1024_1(0())
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          10() -> double(s(double(s(s(0())))))
          1024_1(x) -> if(lt(x,10()),x)
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          if(false(),x) -> s(0())
          if(true(),x) -> double(1024_1(s(x)))
          lt(x,0()) -> false()
          lt(0(),s(y)) -> true()
          lt(s(x),s(y)) -> lt(x,y)
          10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
          1024#() -> c_2(1024_1#(0()))
          1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
          double#(0()) -> c_4()
          double#(s(x)) -> c_5(double#(x))
          if#(false(),x) -> c_6()
          if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
          lt#(x,0()) -> c_8()
          lt#(0(),s(y)) -> c_9()
          lt#(s(x),s(y)) -> c_10(lt#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            1024#() -> c_2(1024_1#(0()))
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            double#(0()) -> c_4()
            double#(s(x)) -> c_5(double#(x))
            if#(false(),x) -> c_6()
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(x,0()) -> c_8()
            lt#(0(),s(y)) -> c_9()
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4,6,8,9}
        by application of
          Pre({4,6,8,9}) = {3,5,7,10}.
        Here rules are labelled as follows:
          1: 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
          2: 1024#() -> c_2(1024_1#(0()))
          3: 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
          4: double#(0()) -> c_4()
          5: double#(s(x)) -> c_5(double#(x))
          6: if#(false(),x) -> c_6()
          7: if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
          8: lt#(x,0()) -> c_8()
          9: lt#(0(),s(y)) -> c_9()
          10: lt#(s(x),s(y)) -> c_10(lt#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            1024#() -> c_2(1024_1#(0()))
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            double#(s(x)) -> c_5(double#(x))
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak DPs:
            double#(0()) -> c_4()
            if#(false(),x) -> c_6()
            lt#(x,0()) -> c_8()
            lt#(0(),s(y)) -> c_9()
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
             -->_2 double#(s(x)) -> c_5(double#(x)):4
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          2:S:1024#() -> c_2(1024_1#(0()))
             -->_1 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):3
          
          3:S:1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
             -->_2 lt#(s(x),s(y)) -> c_10(lt#(x,y)):6
             -->_1 if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x))):5
             -->_2 lt#(0(),s(y)) -> c_9():10
             -->_2 lt#(x,0()) -> c_8():9
             -->_1 if#(false(),x) -> c_6():8
             -->_3 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0())))):1
          
          4:S:double#(s(x)) -> c_5(double#(x))
             -->_1 double#(0()) -> c_4():7
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          5:S:if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
             -->_1 double#(0()) -> c_4():7
             -->_1 double#(s(x)) -> c_5(double#(x)):4
             -->_2 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):3
          
          6:S:lt#(s(x),s(y)) -> c_10(lt#(x,y))
             -->_1 lt#(0(),s(y)) -> c_9():10
             -->_1 lt#(x,0()) -> c_8():9
             -->_1 lt#(s(x),s(y)) -> c_10(lt#(x,y)):6
          
          7:W:double#(0()) -> c_4()
             
          
          8:W:if#(false(),x) -> c_6()
             
          
          9:W:lt#(x,0()) -> c_8()
             
          
          10:W:lt#(0(),s(y)) -> c_9()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: if#(false(),x) -> c_6()
          9: lt#(x,0()) -> c_8()
          10: lt#(0(),s(y)) -> c_9()
          7: double#(0()) -> c_4()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            1024#() -> c_2(1024_1#(0()))
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            double#(s(x)) -> c_5(double#(x))
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
           -->_2 double#(s(x)) -> c_5(double#(x)):4
           -->_1 double#(s(x)) -> c_5(double#(x)):4
        
        2:S:1024#() -> c_2(1024_1#(0()))
           -->_1 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):3
        
        3:S:1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
           -->_2 lt#(s(x),s(y)) -> c_10(lt#(x,y)):6
           -->_1 if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x))):5
           -->_3 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0())))):1
        
        4:S:double#(s(x)) -> c_5(double#(x))
           -->_1 double#(s(x)) -> c_5(double#(x)):4
        
        5:S:if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
           -->_1 double#(s(x)) -> c_5(double#(x)):4
           -->_2 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):3
        
        6:S:lt#(s(x),s(y)) -> c_10(lt#(x,y))
           -->_1 lt#(s(x),s(y)) -> c_10(lt#(x,y)):6
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(2,1024#() -> c_2(1024_1#(0())))]
* Step 6: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            double#(s(x)) -> c_5(double#(x))
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
              double#(s(x)) -> c_5(double#(x))
          - Weak DPs:
              1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
              if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
              lt#(s(x),s(y)) -> c_10(lt#(x,y))
          - Weak TRS:
              10() -> double(s(double(s(s(0())))))
              1024_1(x) -> if(lt(x,10()),x)
              double(0()) -> 0()
              double(s(x)) -> s(s(double(x)))
              if(false(),x) -> s(0())
              if(true(),x) -> double(1024_1(s(x)))
              lt(x,0()) -> false()
              lt(0(),s(y)) -> true()
              lt(s(x),s(y)) -> lt(x,y)
          - Signature:
              {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
              ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
              ,false,s,true}
        
        Problem (S)
          - Strict DPs:
              1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
              if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
              lt#(s(x),s(y)) -> c_10(lt#(x,y))
          - Weak DPs:
              10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
              double#(s(x)) -> c_5(double#(x))
          - Weak TRS:
              10() -> double(s(double(s(s(0())))))
              1024_1(x) -> if(lt(x,10()),x)
              double(0()) -> 0()
              double(s(x)) -> s(s(double(x)))
              if(false(),x) -> s(0())
              if(true(),x) -> double(1024_1(s(x)))
              lt(x,0()) -> false()
              lt(0(),s(y)) -> true()
              lt(s(x),s(y)) -> lt(x,y)
          - Signature:
              {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
              ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
              ,false,s,true}
** Step 6.a:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            double#(s(x)) -> c_5(double#(x))
        - Weak DPs:
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
             -->_2 double#(s(x)) -> c_5(double#(x)):4
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          3:W:1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
             -->_3 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0())))):1
             -->_2 lt#(s(x),s(y)) -> c_10(lt#(x,y)):6
             -->_1 if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x))):5
          
          4:S:double#(s(x)) -> c_5(double#(x))
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          5:W:if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
             -->_2 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):3
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          6:W:lt#(s(x),s(y)) -> c_10(lt#(x,y))
             -->_1 lt#(s(x),s(y)) -> c_10(lt#(x,y)):6
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: lt#(s(x),s(y)) -> c_10(lt#(x,y))
** Step 6.a:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            double#(s(x)) -> c_5(double#(x))
        - Weak DPs:
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
             -->_2 double#(s(x)) -> c_5(double#(x)):4
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          3:W:1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
             -->_3 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0())))):1
             -->_1 if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x))):5
          
          4:S:double#(s(x)) -> c_5(double#(x))
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
          5:W:if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
             -->_2 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):3
             -->_1 double#(s(x)) -> c_5(double#(x)):4
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          1024_1#(x) -> c_3(if#(lt(x,10()),x),10#())
** Step 6.a:3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
          double#(s(x)) -> c_5(double#(x))
      - Weak DPs:
          1024_1#(x) -> c_3(if#(lt(x,10()),x),10#())
          if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
      - Weak TRS:
          10() -> double(s(double(s(s(0())))))
          1024_1(x) -> if(lt(x,10()),x)
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          if(false(),x) -> s(0())
          if(true(),x) -> double(1024_1(s(x)))
          lt(x,0()) -> false()
          lt(0(),s(y)) -> true()
          lt(s(x),s(y)) -> lt(x,y)
      - Signature:
          {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
          ,true/0,c_1/2,c_2/1,c_3/2,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
          ,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 6.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak DPs:
            10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
            double#(s(x)) -> c_5(double#(x))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
             -->_3 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0())))):4
             -->_2 lt#(s(x),s(y)) -> c_10(lt#(x,y)):3
             -->_1 if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x))):2
          
          2:S:if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
             -->_1 double#(s(x)) -> c_5(double#(x)):5
             -->_2 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):1
          
          3:S:lt#(s(x),s(y)) -> c_10(lt#(x,y))
             -->_1 lt#(s(x),s(y)) -> c_10(lt#(x,y)):3
          
          4:W:10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
             -->_2 double#(s(x)) -> c_5(double#(x)):5
             -->_1 double#(s(x)) -> c_5(double#(x)):5
          
          5:W:double#(s(x)) -> c_5(double#(x))
             -->_1 double#(s(x)) -> c_5(double#(x)):5
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: 10#() -> c_1(double#(s(double(s(s(0()))))),double#(s(s(0()))))
          5: double#(s(x)) -> c_5(double#(x))
** Step 6.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
            if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/3,c_4/0,c_5/1,c_6/0,c_7/2,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#())
             -->_2 lt#(s(x),s(y)) -> c_10(lt#(x,y)):3
             -->_1 if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x))):2
          
          2:S:if#(true(),x) -> c_7(double#(1024_1(s(x))),1024_1#(s(x)))
             -->_2 1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()),10#()):1
          
          3:S:lt#(s(x),s(y)) -> c_10(lt#(x,y))
             -->_1 lt#(s(x),s(y)) -> c_10(lt#(x,y)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()))
          if#(true(),x) -> c_7(1024_1#(s(x)))
** Step 6.b:3: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()))
            if#(true(),x) -> c_7(1024_1#(s(x)))
            lt#(s(x),s(y)) -> c_10(lt#(x,y))
        - Weak TRS:
            10() -> double(s(double(s(s(0())))))
            1024_1(x) -> if(lt(x,10()),x)
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            if(false(),x) -> s(0())
            if(true(),x) -> double(1024_1(s(x)))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
            ,true/0,c_1/2,c_2/1,c_3/2,c_4/0,c_5/1,c_6/0,c_7/1,c_8/0,c_9/0,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
            ,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          10() -> double(s(double(s(s(0())))))
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          lt(x,0()) -> false()
          lt(0(),s(y)) -> true()
          lt(s(x),s(y)) -> lt(x,y)
          1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()))
          if#(true(),x) -> c_7(1024_1#(s(x)))
          lt#(s(x),s(y)) -> c_10(lt#(x,y))
** Step 6.b:4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          1024_1#(x) -> c_3(if#(lt(x,10()),x),lt#(x,10()))
          if#(true(),x) -> c_7(1024_1#(s(x)))
          lt#(s(x),s(y)) -> c_10(lt#(x,y))
      - Weak TRS:
          10() -> double(s(double(s(s(0())))))
          double(0()) -> 0()
          double(s(x)) -> s(s(double(x)))
          lt(x,0()) -> false()
          lt(0(),s(y)) -> true()
          lt(s(x),s(y)) -> lt(x,y)
      - Signature:
          {10/0,1024/0,1024_1/1,double/1,if/2,lt/2,10#/0,1024#/0,1024_1#/1,double#/1,if#/2,lt#/2} / {0/0,false/0,s/1
          ,true/0,c_1/2,c_2/1,c_3/2,c_4/0,c_5/1,c_6/0,c_7/1,c_8/0,c_9/0,c_10/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {10#,1024#,1024_1#,double#,if#,lt#} and constructors {0
          ,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE