* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { insert[Ite](<(S(x),x),S(x),r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { Cons(x,y)} =
            isort(Cons(x,y),z) ->^+ isort(y,insert(x,z))
              = C[isort(y,insert(x,z)) = isort(y,z){z -> insert(x,z)}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
          inssort#(xs) -> c_2(isort#(xs,Nil()))
          isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          isort#(Nil(),r) -> c_4()
        Weak DPs
          <#(x,0()) -> c_5()
          <#(0(),S(y)) -> c_6()
          <#(S(x),S(y)) -> c_7(<#(x,y))
          insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
          insert[Ite]#(True(),x,r) -> c_9()
        
        and mark the set of starting terms.
** Step 1.b:2: UsableRules WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
            inssort#(xs) -> c_2(isort#(xs,Nil()))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
            isort#(Nil(),r) -> c_4()
        - Weak DPs:
            <#(x,0()) -> c_5()
            <#(0(),S(y)) -> c_6()
            <#(S(x),S(y)) -> c_7(<#(x,y))
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            insert[Ite]#(True(),x,r) -> c_9()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
            inssort(xs) -> isort(xs,Nil())
            isort(Cons(x,xs),r) -> isort(xs,insert(x,r))
            isort(Nil(),r) -> Nil()
        - Signature:
            { False()
          <(0(),S(y)) -> True()
          <(S(x),S(y)) -> <(x,y)
          insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
          insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
          insert[Ite](True(),x,r) -> Cons(x,r)
          <#(x,0()) -> c_5()
          <#(0(),S(y)) -> c_6()
          <#(S(x),S(y)) -> c_7(<#(x,y))
          insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
          insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
          insert[Ite]#(True(),x,r) -> c_9()
          inssort#(xs) -> c_2(isort#(xs,Nil()))
          isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          isort#(Nil(),r) -> c_4()
** Step 1.b:3: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
            inssort#(xs) -> c_2(isort#(xs,Nil()))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
            isort#(Nil(),r) -> c_4()
        - Weak DPs:
            <#(x,0()) -> c_5()
            <#(0(),S(y)) -> c_6()
            <#(S(x),S(y)) -> c_7(<#(x,y))
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            insert[Ite]#(True(),x,r) -> c_9()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
          2: inssort#(xs) -> c_2(isort#(xs,Nil()))
          3: isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          4: isort#(Nil(),r) -> c_4()
          5: <#(x,0()) -> c_5()
          6: <#(0(),S(y)) -> c_6()
          7: <#(S(x),S(y)) -> c_7(<#(x,y))
          8: insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
          9: insert[Ite]#(True(),x,r) -> c_9()
** Step 1.b:4: RemoveWeakSuffixes WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
            inssort#(xs) -> c_2(isort#(xs,Nil()))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak DPs:
            <#(x,0()) -> c_5()
            <#(0(),S(y)) -> c_6()
            <#(S(x),S(y)) -> c_7(<#(x,y))
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            insert[Ite]#(True(),x,r) -> c_9()
            isort#(Nil(),r) -> c_4()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
             -->_1 insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs)):7
             -->_2 <#(S(x),S(y)) -> c_7(<#(x,y)):6
             -->_1 insert[Ite]#(True(),x,r) -> c_9():8
             -->_2 <#(x,0()) -> c_5():4
          
          2:S:inssort#(xs) -> c_2(isort#(xs,Nil()))
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
             -->_1 isort#(Nil(),r) -> c_4():9
          
          3:S:isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
             -->_1 isort#(Nil(),r) -> c_4():9
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
             -->_2 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x)):1
          
          4:W:<#(x,0()) -> c_5()
             
          
          5:W:<#(0(),S(y)) -> c_6()
             
          
          6:W:<#(S(x),S(y)) -> c_7(<#(x,y))
             -->_1 <#(S(x),S(y)) -> c_7(<#(x,y)):6
             -->_1 <#(0(),S(y)) -> c_6():5
             -->_1 <#(x,0()) -> c_5():4
          
          7:W:insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
             -->_1 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x)):1
          
          8:W:insert[Ite]#(True(),x,r) -> c_9()
             
          
          9:W:isort#(Nil(),r) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: isort#(Nil(),r) -> c_4()
          8: insert[Ite]#(True(),x,r) -> c_9()
          6: <#(S(x),S(y)) -> c_7(<#(x,y))
          4: <#(x,0()) -> c_5()
          5: <#(0(),S(y)) -> c_6()
** Step 1.b:5: SimplifyRHS WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
            inssort#(xs) -> c_2(isort#(xs,Nil()))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak DPs:
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x))
             -->_1 insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs)):7
          
          2:S:inssort#(xs) -> c_2(isort#(xs,Nil()))
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
          
          3:S:isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
             -->_2 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x)):1
          
          7:W:insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
             -->_1 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r),<#(S(x),x)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
** Step 1.b:6: RemoveHeads WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
            inssort#(xs) -> c_2(isort#(xs,Nil()))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak DPs:
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r))
           -->_1 insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs)):4
        
        2:S:inssort#(xs) -> c_2(isort#(xs,Nil()))
           -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
        
        3:S:isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
           -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
           -->_2 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r)):1
        
        4:W:insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
           -->_1 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r)):1
        
        
        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,inssort#(xs) -> c_2(isort#(xs,Nil())))]
** Step 1.b:7: Decompose WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak DPs:
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r))
          - Weak DPs:
              insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
              isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          - Weak TRS:
              <(x,0()) -> False()
              <(0(),S(y)) -> True()
              <(S(x),S(y)) -> <(x,y)
              insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
              insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
              insert[Ite](True(),x,r) -> Cons(x,r)
          - Signature:
              { c_3(isort#(xs,insert(x,r)),insert#(x,r))
          - Weak DPs:
              insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
              insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
          - Weak TRS:
              <(x,0()) -> False()
              <(0(),S(y)) -> True()
              <(S(x),S(y)) -> <(x,y)
              insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
              insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
              insert[Ite](True(),x,r) -> Cons(x,r)
          - Signature:
              { c_1(insert[Ite]#(<(S(x),x),S(x),r))
        - Weak DPs:
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r))
          
        Consider the set of all dependency pairs
          1: insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
          3: isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          4: insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
        Processor NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^2))
        SPACE(?,?)on application of the dependency pairs
          {1}
        These cover all (indirect) predecessors of dependency pairs
          {1,4}
        their number of applications is equally bounded.
        The dependency pairs are shifted into the weak component.
**** Step 1.b:7.a:1.a:1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
        - Weak DPs:
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { 2 + r                              
                        = c_1(insert[Ite]#(<(S(x),x),S(x),r))
        
        
        Following rules are (at-least) weakly oriented:
        insert[Ite]#(False(),x',Cons(x,xs)) =  1 + x + x' + x'^2 + xs                               
                                            >= 1 + x' + x'^2 + xs                                   
                                            =  c_8(insert#(x',xs))                                  
        
                       isort#(Cons(x,xs),r) =  3 + r + r*x + r*xs + 2*x + 2*x*xs + x^2 + 2*xs + xs^2
                                            >= 3 + r + r*xs + x + 2*x*xs + x^2 + xs + xs^2          
                                            =  c_3(isort#(xs,insert(x,r)),insert#(x,r))             
        
                             insert(S(x),r) =  3 + r                                                
                                            >= 3 + r                                                
                                            =  insert[Ite](<(S(x),x),S(x),r)                        
        
         insert[Ite](False(),x',Cons(x,xs)) =  2 + x + 2*x' + xs                                    
                                            >= 2 + x + 2*x' + xs                                    
                                            =  Cons(x,insert(x',xs))                                
        
                    insert[Ite](True(),x,r) =  1 + r + 2*x                                          
                                            >= 1 + r + x                                            
                                            =  Cons(x,r)                                            
        
**** Step 1.b:7.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r))
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_1(insert[Ite]#(<(S(x),x),S(x),r))
             -->_1 insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs)):2
          
          2:W:insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
             -->_1 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r)):1
          
          3:W:isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):3
             -->_2 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
          1: insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
          2: insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
**** Step 1.b:7.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak DPs:
            insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
            insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_3(isort#(xs,insert(x,r)),insert#(x,r))
             -->_2 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r)):2
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):1
          
          2:W:insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
             -->_1 insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs)):3
          
          3:W:insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
             -->_1 insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: insert#(S(x),r) -> c_1(insert[Ite]#(<(S(x),x),S(x),r))
          3: insert[Ite]#(False(),x',Cons(x,xs)) -> c_8(insert#(x',xs))
*** Step 1.b:7.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_3(isort#(xs,insert(x,r)),insert#(x,r))
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)),insert#(x,r)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)))
*** Step 1.b:7.b:3: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_3(isort#(xs,insert(x,r)))
          
        The strictly oriented rules are moved into the weak component.
**** Step 1.b:7.b:3.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { [2] xs + [19]              
                             = c_3(isort#(xs,insert(x,r)))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 1.b:7.b:3.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_3(isort#(xs,insert(x,r)))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            { c_3(isort#(xs,insert(x,r)))
             -->_1 isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r))):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: isort#(Cons(x,xs),r) -> c_3(isort#(xs,insert(x,r)))
**** Step 1.b:7.b:3.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            insert(S(x),r) -> insert[Ite](<(S(x),x),S(x),r)
            insert[Ite](False(),x',Cons(x,xs)) -> Cons(x,insert(x',xs))
            insert[Ite](True(),x,r) -> Cons(x,r)
        - Signature:
            {