MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
          a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
          a#(h(),h(),x) -> c_3()
          a#(s(x),h(),z) -> c_4(a#(x,z,z))
          app#(l,nil()) -> c_5()
          app#(cons(x,l),k) -> c_6(app#(l,k))
          app#(nil(),k) -> c_7()
          sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
          sum#(cons(x,nil())) -> c_9()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(h(),h(),x) -> c_3()
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
            app#(l,nil()) -> c_5()
            app#(cons(x,l),k) -> c_6(app#(l,k))
            app#(nil(),k) -> c_7()
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
            sum#(cons(x,nil())) -> c_9()
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          a(x,s(y),h()) -> a(x,y,s(h()))
          a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
          a(h(),h(),x) -> s(x)
          a(s(x),h(),z) -> a(x,z,z)
          a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
          a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
          a#(h(),h(),x) -> c_3()
          a#(s(x),h(),z) -> c_4(a#(x,z,z))
          app#(l,nil()) -> c_5()
          app#(cons(x,l),k) -> c_6(app#(l,k))
          app#(nil(),k) -> c_7()
          sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
          sum#(cons(x,nil())) -> c_9()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(h(),h(),x) -> c_3()
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
            app#(l,nil()) -> c_5()
            app#(cons(x,l),k) -> c_6(app#(l,k))
            app#(nil(),k) -> c_7()
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
            sum#(cons(x,nil())) -> c_9()
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,5,7,9}
        by application of
          Pre({3,5,7,9}) = {1,2,4,6,8}.
        Here rules are labelled as follows:
          1: a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
          2: a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
          3: a#(h(),h(),x) -> c_3()
          4: a#(s(x),h(),z) -> c_4(a#(x,z,z))
          5: app#(l,nil()) -> c_5()
          6: app#(cons(x,l),k) -> c_6(app#(l,k))
          7: app#(nil(),k) -> c_7()
          8: sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
          9: sum#(cons(x,nil())) -> c_9()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
            app#(cons(x,l),k) -> c_6(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak DPs:
            a#(h(),h(),x) -> c_3()
            app#(l,nil()) -> c_5()
            app#(nil(),k) -> c_7()
            sum#(cons(x,nil())) -> c_9()
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
             -->_1 a#(h(),h(),x) -> c_3():6
          
          2:S:a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_1 a#(h(),h(),x) -> c_3():6
             -->_2 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
             -->_2 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):1
             -->_1 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):1
          
          3:S:a#(s(x),h(),z) -> c_4(a#(x,z,z))
             -->_1 a#(h(),h(),x) -> c_3():6
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
          
          4:S:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(nil(),k) -> c_7():8
             -->_1 app#(l,nil()) -> c_5():7
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):4
          
          5:S:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
             -->_1 sum#(cons(x,nil())) -> c_9():9
             -->_2 a#(h(),h(),x) -> c_3():6
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h())):5
             -->_2 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_2 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):1
          
          6:W:a#(h(),h(),x) -> c_3()
             
          
          7:W:app#(l,nil()) -> c_5()
             
          
          8:W:app#(nil(),k) -> c_7()
             
          
          9:W:sum#(cons(x,nil())) -> c_9()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: sum#(cons(x,nil())) -> c_9()
          7: app#(l,nil()) -> c_5()
          8: app#(nil(),k) -> c_7()
          6: a#(h(),h(),x) -> c_3()
* Step 5: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
            app#(cons(x,l),k) -> c_6(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + 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:
              a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
              a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
              a#(s(x),h(),z) -> c_4(a#(x,z,z))
          - Weak DPs:
              app#(cons(x,l),k) -> c_6(app#(l,k))
              sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
          - Weak TRS:
              a(x,s(y),h()) -> a(x,y,s(h()))
              a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
              a(h(),h(),x) -> s(x)
              a(s(x),h(),z) -> a(x,z,z)
          - Signature:
              {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0
              ,c_8/2,c_9/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
        
        Problem (S)
          - Strict DPs:
              app#(cons(x,l),k) -> c_6(app#(l,k))
              sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
          - Weak DPs:
              a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
              a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
              a#(s(x),h(),z) -> c_4(a#(x,z,z))
          - Weak TRS:
              a(x,s(y),h()) -> a(x,y,s(h()))
              a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
              a(h(),h(),x) -> s(x)
              a(s(x),h(),z) -> a(x,z,z)
          - Signature:
              {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0
              ,c_8/2,c_9/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
** Step 5.a:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
        - Weak DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
          
          2:S:a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
             -->_2 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):1
             -->_1 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):1
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_2 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
          
          3:S:a#(s(x),h(),z) -> c_4(a#(x,z,z))
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):2
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
          
          4:W:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):4
          
          5:W:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
             -->_2 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):1
             -->_2 a#(s(x),h(),z) -> c_4(a#(x,z,z)):3
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h())):5
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: app#(cons(x,l),k) -> c_6(app#(l,k))
** Step 5.a:2: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
        - Weak DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        and a lower component
          a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
          a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
          a#(s(x),h(),z) -> c_4(a#(x,z,z))
        Further, following extension rules are added to the lower component.
          sum#(cons(x,cons(y,l))) -> a#(x,y,h())
          sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
*** Step 5.a:2.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.a:2.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {a#,app#,sum#}
        TcT has computed the following interpretation:
             p(a) = [1] x1 + [3] x2 + [8]
           p(app) = [2] x1 + [0]         
          p(cons) = [1] x2 + [2]         
             p(h) = [1]                  
           p(nil) = [1]                  
             p(s) = [1] x1 + [7]         
           p(sum) = [1]                  
            p(a#) = [1] x3 + [0]         
          p(app#) = [1] x1 + [2]         
          p(sum#) = [4] x1 + [4]         
           p(c_1) = [1]                  
           p(c_2) = [1] x1 + [1] x2 + [1]
           p(c_3) = [1]                  
           p(c_4) = [2] x1 + [1]         
           p(c_5) = [2]                  
           p(c_6) = [1] x1 + [1]         
           p(c_7) = [1]                  
           p(c_8) = [1] x1 + [1] x2 + [0]
           p(c_9) = [0]                  
        
        Following rules are strictly oriented:
        sum#(cons(x,cons(y,l))) = [4] l + [20]                             
                                > [4] l + [13]                             
                                = c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.a:2.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.a:2.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h())):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
**** Step 5.a:2.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 5.a:2.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
          a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
          a#(s(x),h(),z) -> c_4(a#(x,z,z))
      - Weak DPs:
          sum#(cons(x,cons(y,l))) -> a#(x,y,h())
          sum#(cons(x,cons(y,l))) -> sum#(cons(a(x,y,h()),l))
      - Weak TRS:
          a(x,s(y),h()) -> a(x,y,s(h()))
          a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
          a(h(),h(),x) -> s(x)
          a(s(x),h(),z) -> a(x,z,z)
      - Signature:
          {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
          ,c_9/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 5.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak DPs:
            a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
            a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
            a#(s(x),h(),z) -> c_4(a#(x,z,z))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):1
          
          2:S:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
             -->_2 a#(s(x),h(),z) -> c_4(a#(x,z,z)):5
             -->_2 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):3
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h())):2
          
          3:W:a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):5
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):4
          
          4:W:a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):5
             -->_2 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):4
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):4
             -->_2 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):3
             -->_1 a#(x,s(y),h()) -> c_1(a#(x,y,s(h()))):3
          
          5:W:a#(s(x),h(),z) -> c_4(a#(x,z,z))
             -->_1 a#(s(x),h(),z) -> c_4(a#(x,z,z)):5
             -->_1 a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z)):4
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: a#(s(x),h(),z) -> c_4(a#(x,z,z))
          4: a#(x,s(y),s(z)) -> c_2(a#(x,y,a(x,s(y),z)),a#(x,s(y),z))
          3: a#(x,s(y),h()) -> c_1(a#(x,y,s(h())))
** Step 5.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):1
          
          2:S:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h()))
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)),a#(x,y,h())):2
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
** Step 5.b:3: Decompose WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + 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:
              app#(cons(x,l),k) -> c_6(app#(l,k))
          - Weak DPs:
              sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
          - Weak TRS:
              a(x,s(y),h()) -> a(x,y,s(h()))
              a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
              a(h(),h(),x) -> s(x)
              a(s(x),h(),z) -> a(x,z,z)
          - Signature:
              {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0
              ,c_8/1,c_9/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
        
        Problem (S)
          - Strict DPs:
              sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
          - Weak DPs:
              app#(cons(x,l),k) -> c_6(app#(l,k))
          - Weak TRS:
              a(x,s(y),h()) -> a(x,y,s(h()))
              a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
              a(h(),h(),x) -> s(x)
              a(s(x),h(),z) -> a(x,z,z)
          - Signature:
              {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0
              ,c_8/1,c_9/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
*** Step 5.b:3.a:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Weak DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):1
          
          2:W:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l))):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
*** Step 5.b:3.a:2: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          app#(cons(x,l),k) -> c_6(app#(l,k))
*** Step 5.b:3.a:3: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: app#(cons(x,l),k) -> c_6(app#(l,k))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.b:3.a:3.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {a#,app#,sum#}
        TcT has computed the following interpretation:
             p(a) = [1]                  
           p(app) = [1]                  
          p(cons) = [1] x2 + [4]         
             p(h) = [0]                  
           p(nil) = [0]                  
             p(s) = [1] x1 + [1]         
           p(sum) = [4] x1 + [0]         
            p(a#) = [2] x3 + [8]         
          p(app#) = [4] x1 + [8] x2 + [8]
          p(sum#) = [1] x1 + [1]         
           p(c_1) = [1] x1 + [4]         
           p(c_2) = [1] x1 + [1] x2 + [0]
           p(c_3) = [8]                  
           p(c_4) = [2] x1 + [0]         
           p(c_5) = [1]                  
           p(c_6) = [1] x1 + [8]         
           p(c_7) = [0]                  
           p(c_8) = [8]                  
           p(c_9) = [0]                  
        
        Following rules are strictly oriented:
        app#(cons(x,l),k) = [8] k + [4] l + [24]
                          > [8] k + [4] l + [16]
                          = c_6(app#(l,k))      
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.b:3.a:3.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.b:3.a:3.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: app#(cons(x,l),k) -> c_6(app#(l,k))
**** Step 5.b:3.a:3.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 5.b:3.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak DPs:
            app#(cons(x,l),k) -> c_6(app#(l,k))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l))):1
          
          2:W:app#(cons(x,l),k) -> c_6(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_6(app#(l,k)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: app#(cons(x,l),k) -> c_6(app#(l,k))
*** Step 5.b:3.b:2: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.b:3.b:2.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_8) = {1}
        
        Following symbols are considered usable:
          {a#,app#,sum#}
        TcT has computed the following interpretation:
             p(a) = [2] x3 + [0]         
           p(app) = [1] x1 + [1] x2 + [4]
          p(cons) = [1] x2 + [1]         
             p(h) = [0]                  
           p(nil) = [4]                  
             p(s) = [3]                  
           p(sum) = [1] x1 + [0]         
            p(a#) = [1] x1 + [4] x3 + [2]
          p(app#) = [4] x1 + [1]         
          p(sum#) = [8] x1 + [0]         
           p(c_1) = [1]                  
           p(c_2) = [2] x1 + [2] x2 + [0]
           p(c_3) = [0]                  
           p(c_4) = [2]                  
           p(c_5) = [1]                  
           p(c_6) = [1] x1 + [1]         
           p(c_7) = [0]                  
           p(c_8) = [1] x1 + [7]         
           p(c_9) = [0]                  
        
        Following rules are strictly oriented:
        sum#(cons(x,cons(y,l))) = [8] l + [16]                 
                                > [8] l + [15]                 
                                = c_8(sum#(cons(a(x,y,h()),l)))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.b:3.b:2.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.b:3.b:2.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
             -->_1 sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l))):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: sum#(cons(x,cons(y,l))) -> c_8(sum#(cons(a(x,y,h()),l)))
**** Step 5.b:3.b:2.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(x,s(y),h()) -> a(x,y,s(h()))
            a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
            a(h(),h(),x) -> s(x)
            a(s(x),h(),z) -> a(x,z,z)
        - Signature:
            {a/3,app/2,sum/1,a#/3,app#/2,sum#/1} / {cons/2,h/0,nil/0,s/1,c_1/1,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1
            ,c_9/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,app#,sum#} and constructors {cons,h,nil,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

MAYBE