MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            +(x,h()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(h(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            s(h()) -> 1()
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1} / {1/0,cons/2,h/0,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,a,app,s,sum} and constructors {1,cons,h,nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          +#(x,h()) -> c_1()
          +#(+(x,y),z) -> c_2(+#(x,+(y,z)),+#(y,z))
          +#(h(),x) -> c_3()
          +#(s(x),s(y)) -> c_4(s#(s(+(x,y))),s#(+(x,y)),+#(x,y))
          a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
          a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
          a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
          a#(h(),h(),h(),x) -> c_8(s#(x))
          a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
          app#(l,nil()) -> c_10()
          app#(cons(x,l),k) -> c_11(app#(l,k))
          app#(nil(),k) -> c_12()
          s#(h()) -> c_13()
          sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
          sum#(cons(x,nil())) -> c_15()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,h()) -> c_1()
            +#(+(x,y),z) -> c_2(+#(x,+(y,z)),+#(y,z))
            +#(h(),x) -> c_3()
            +#(s(x),s(y)) -> c_4(s#(s(+(x,y))),s#(+(x,y)),+#(x,y))
            a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
            a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
            a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
            a#(h(),h(),h(),x) -> c_8(s#(x))
            a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
            app#(l,nil()) -> c_10()
            app#(cons(x,l),k) -> c_11(app#(l,k))
            app#(nil(),k) -> c_12()
            s#(h()) -> c_13()
            sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
            sum#(cons(x,nil())) -> c_15()
        - Weak TRS:
            +(x,h()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(h(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            app(l,nil()) -> l
            app(cons(x,l),k) -> cons(x,app(l,k))
            app(nil(),k) -> k
            s(h()) -> 1()
            sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h(),h()),l))
            sum(cons(x,nil())) -> cons(x,nil())
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1,+#/2,a#/4,app#/2,s#/1,sum#/1} / {1/0,cons/2,h/0,nil/0,c_1/0,c_2/2,c_3/0,c_4/3,c_5/2
            ,c_6/3,c_7/1,c_8/1,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0,c_14/2,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,a#,app#,s#,sum#} and constructors {1,cons,h,nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          a(l,x,s(y),h()) -> a(l,x,y,s(h()))
          a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
          a(l,s(x),h(),z) -> a(l,x,z,z)
          a(h(),h(),h(),x) -> s(x)
          a(s(l),h(),h(),z) -> a(l,z,h(),z)
          s(h()) -> 1()
          +#(x,h()) -> c_1()
          +#(h(),x) -> c_3()
          a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
          a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
          a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
          a#(h(),h(),h(),x) -> c_8(s#(x))
          a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
          app#(l,nil()) -> c_10()
          app#(cons(x,l),k) -> c_11(app#(l,k))
          app#(nil(),k) -> c_12()
          s#(h()) -> c_13()
          sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
          sum#(cons(x,nil())) -> c_15()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            +#(x,h()) -> c_1()
            +#(h(),x) -> c_3()
            a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
            a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
            a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
            a#(h(),h(),h(),x) -> c_8(s#(x))
            a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
            app#(l,nil()) -> c_10()
            app#(cons(x,l),k) -> c_11(app#(l,k))
            app#(nil(),k) -> c_12()
            s#(h()) -> c_13()
            sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
            sum#(cons(x,nil())) -> c_15()
        - Weak TRS:
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            s(h()) -> 1()
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1,+#/2,a#/4,app#/2,s#/1,sum#/1} / {1/0,cons/2,h/0,nil/0,c_1/0,c_2/2,c_3/0,c_4/3,c_5/2
            ,c_6/3,c_7/1,c_8/1,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0,c_14/2,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,a#,app#,s#,sum#} and constructors {1,cons,h,nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,8,10,11,13}
        by application of
          Pre({1,2,8,10,11,13}) = {3,4,6,9,12}.
        Here rules are labelled as follows:
          1: +#(x,h()) -> c_1()
          2: +#(h(),x) -> c_3()
          3: a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
          4: a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
          5: a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
          6: a#(h(),h(),h(),x) -> c_8(s#(x))
          7: a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
          8: app#(l,nil()) -> c_10()
          9: app#(cons(x,l),k) -> c_11(app#(l,k))
          10: app#(nil(),k) -> c_12()
          11: s#(h()) -> c_13()
          12: sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
          13: sum#(cons(x,nil())) -> c_15()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
            a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
            a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
            a#(h(),h(),h(),x) -> c_8(s#(x))
            a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
            app#(cons(x,l),k) -> c_11(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
        - Weak DPs:
            +#(x,h()) -> c_1()
            +#(h(),x) -> c_3()
            app#(l,nil()) -> c_10()
            app#(nil(),k) -> c_12()
            s#(h()) -> c_13()
            sum#(cons(x,nil())) -> c_15()
        - Weak TRS:
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            s(h()) -> 1()
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1,+#/2,a#/4,app#/2,s#/1,sum#/1} / {1/0,cons/2,h/0,nil/0,c_1/0,c_2/2,c_3/0,c_4/3,c_5/2
            ,c_6/3,c_7/1,c_8/1,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0,c_14/2,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,a#,app#,s#,sum#} and constructors {1,cons,h,nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4}
        by application of
          Pre({4}) = {1,2,5,7}.
        Here rules are labelled as follows:
          1: a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
          2: a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
          3: a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
          4: a#(h(),h(),h(),x) -> c_8(s#(x))
          5: a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
          6: app#(cons(x,l),k) -> c_11(app#(l,k))
          7: sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
          8: +#(x,h()) -> c_1()
          9: +#(h(),x) -> c_3()
          10: app#(l,nil()) -> c_10()
          11: app#(nil(),k) -> c_12()
          12: s#(h()) -> c_13()
          13: sum#(cons(x,nil())) -> c_15()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
            a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
            a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
            a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
            app#(cons(x,l),k) -> c_11(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
        - Weak DPs:
            +#(x,h()) -> c_1()
            +#(h(),x) -> c_3()
            a#(h(),h(),h(),x) -> c_8(s#(x))
            app#(l,nil()) -> c_10()
            app#(nil(),k) -> c_12()
            s#(h()) -> c_13()
            sum#(cons(x,nil())) -> c_15()
        - Weak TRS:
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            s(h()) -> 1()
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1,+#/2,a#/4,app#/2,s#/1,sum#/1} / {1/0,cons/2,h/0,nil/0,c_1/0,c_2/2,c_3/0,c_4/3,c_5/2
            ,c_6/3,c_7/1,c_8/1,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0,c_14/2,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,a#,app#,s#,sum#} and constructors {1,cons,h,nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
             -->_1 a#(h(),h(),h(),x) -> c_8(s#(x)):9
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_1 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
             -->_2 s#(h()) -> c_13():12
             -->_1 a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h())):1
          
          2:S:a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
             -->_2 a#(h(),h(),h(),x) -> c_8(s#(x)):9
             -->_1 a#(h(),h(),h(),x) -> c_8(s#(x)):9
             -->_2 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_2 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_3 s#(h()) -> c_13():12
             -->_2 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
             -->_1 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
             -->_2 a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h())):1
             -->_1 a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h())):1
          
          3:S:a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_1 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
          
          4:S:a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
             -->_1 a#(h(),h(),h(),x) -> c_8(s#(x)):9
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
          
          5:S:app#(cons(x,l),k) -> c_11(app#(l,k))
             -->_1 app#(nil(),k) -> c_12():11
             -->_1 app#(l,nil()) -> c_10():10
             -->_1 app#(cons(x,l),k) -> c_11(app#(l,k)):5
          
          6:S:sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
             -->_2 a#(h(),h(),h(),x) -> c_8(s#(x)):9
             -->_1 sum#(cons(x,nil())) -> c_15():13
             -->_1 sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h())):6
             -->_2 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_2 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
          
          7:W:+#(x,h()) -> c_1()
             
          
          8:W:+#(h(),x) -> c_3()
             
          
          9:W:a#(h(),h(),h(),x) -> c_8(s#(x))
             -->_1 s#(h()) -> c_13():12
          
          10:W:app#(l,nil()) -> c_10()
             
          
          11:W:app#(nil(),k) -> c_12()
             
          
          12:W:s#(h()) -> c_13()
             
          
          13:W:sum#(cons(x,nil())) -> c_15()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: +#(h(),x) -> c_3()
          7: +#(x,h()) -> c_1()
          13: sum#(cons(x,nil())) -> c_15()
          10: app#(l,nil()) -> c_10()
          11: app#(nil(),k) -> c_12()
          9: a#(h(),h(),h(),x) -> c_8(s#(x))
          12: s#(h()) -> c_13()
* Step 6: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
            a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
            a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
            a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
            app#(cons(x,l),k) -> c_11(app#(l,k))
            sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
        - Weak TRS:
            a(l,x,s(y),h()) -> a(l,x,y,s(h()))
            a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
            a(l,s(x),h(),z) -> a(l,x,z,z)
            a(h(),h(),h(),x) -> s(x)
            a(s(l),h(),h(),z) -> a(l,z,h(),z)
            s(h()) -> 1()
        - Signature:
            {+/2,a/4,app/2,s/1,sum/1,+#/2,a#/4,app#/2,s#/1,sum#/1} / {1/0,cons/2,h/0,nil/0,c_1/0,c_2/2,c_3/0,c_4/3,c_5/2
            ,c_6/3,c_7/1,c_8/1,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0,c_14/2,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,a#,app#,s#,sum#} and constructors {1,cons,h,nil}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h()))
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_1 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
             -->_1 a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h())):1
          
          2:S:a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y))
             -->_2 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_2 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_2 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
             -->_1 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
             -->_2 a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h())):1
             -->_1 a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())),s#(h())):1
          
          3:S:a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
             -->_1 a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z),s#(y)):2
          
          4:S:a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
             -->_1 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_1 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
          
          5:S:app#(cons(x,l),k) -> c_11(app#(l,k))
             -->_1 app#(cons(x,l),k) -> c_11(app#(l,k)):5
          
          6:S:sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
             -->_1 sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h())):6
             -->_2 a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z)):4
             -->_2 a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())))
          a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z))
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          a#(l,x,s(y),h()) -> c_5(a#(l,x,y,s(h())))
          a#(l,x,s(y),s(z)) -> c_6(a#(l,x,y,a(l,x,s(y),z)),a#(l,x,s(y),z))
          a#(l,s(x),h(),z) -> c_7(a#(l,x,z,z))
          a#(s(l),h(),h(),z) -> c_9(a#(l,z,h(),z))
          app#(cons(x,l),k) -> c_11(app#(l,k))
          sum#(cons(x,cons(y,l))) -> c_14(sum#(cons(a(x,y,h(),h()),l)),a#(x,y,h(),h()))
      - Weak TRS:
          a(l,x,s(y),h()) -> a(l,x,y,s(h()))
          a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
          a(l,s(x),h(),z) -> a(l,x,z,z)
          a(h(),h(),h(),x) -> s(x)
          a(s(l),h(),h(),z) -> a(l,z,h(),z)
          s(h()) -> 1()
      - Signature:
          {+/2,a/4,app/2,s/1,sum/1,+#/2,a#/4,app#/2,s#/1,sum#/1} / {1/0,cons/2,h/0,nil/0,c_1/0,c_2/2,c_3/0,c_4/3,c_5/1
          ,c_6/2,c_7/1,c_8/1,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0,c_14/2,c_15/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {+#,a#,app#,s#,sum#} and constructors {1,cons,h,nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE