MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(#(),x) -> #()
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,prod/1,sum/1} / {#/0,1/1,cons/2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,0,prod,sum} and constructors {#,1,cons,nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(#(),x) -> c_1()
          *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
          *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
          +#(x,#()) -> c_4()
          +#(#(),x) -> c_5()
          +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
          +#(0(x),1(y)) -> c_7(+#(x,y))
          +#(1(x),0(y)) -> c_8(+#(x,y))
          +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
          0#(#()) -> c_10()
          prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
          prod#(nil()) -> c_12()
          sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
          sum#(nil()) -> c_14(0#(#()))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(#(),x) -> c_1()
            *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(x,#()) -> c_4()
            +#(#(),x) -> c_5()
            +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_7(+#(x,y))
            +#(1(x),0(y)) -> c_8(+#(x,y))
            +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            0#(#()) -> c_10()
            prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
            prod#(nil()) -> c_12()
            sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
            sum#(nil()) -> c_14(0#(#()))
        - Weak TRS:
            *(#(),x) -> #()
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,prod/1,sum/1,*#/2,+#/2,0#/1,prod#/1,sum#/1} / {#/0,1/1,cons/2,nil/0,c_1/0,c_2/2,c_3/3,c_4/0
            ,c_5/0,c_6/2,c_7/1,c_8/1,c_9/3,c_10/0,c_11/2,c_12/0,c_13/2,c_14/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,0#,prod#,sum#} and constructors {#,1,cons,nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,10,12}
        by application of
          Pre({1,4,5,10,12}) = {2,3,6,7,8,9,11,13,14}.
        Here rules are labelled as follows:
          1: *#(#(),x) -> c_1()
          2: *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
          3: *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
          4: +#(x,#()) -> c_4()
          5: +#(#(),x) -> c_5()
          6: +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
          7: +#(0(x),1(y)) -> c_7(+#(x,y))
          8: +#(1(x),0(y)) -> c_8(+#(x,y))
          9: +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
          10: 0#(#()) -> c_10()
          11: prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
          12: prod#(nil()) -> c_12()
          13: sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
          14: sum#(nil()) -> c_14(0#(#()))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_7(+#(x,y))
            +#(1(x),0(y)) -> c_8(+#(x,y))
            +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
            sum#(nil()) -> c_14(0#(#()))
        - Weak DPs:
            *#(#(),x) -> c_1()
            +#(x,#()) -> c_4()
            +#(#(),x) -> c_5()
            0#(#()) -> c_10()
            prod#(nil()) -> c_12()
        - Weak TRS:
            *(#(),x) -> #()
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,prod/1,sum/1,*#/2,+#/2,0#/1,prod#/1,sum#/1} / {#/0,1/1,cons/2,nil/0,c_1/0,c_2/2,c_3/3,c_4/0
            ,c_5/0,c_6/2,c_7/1,c_8/1,c_9/3,c_10/0,c_11/2,c_12/0,c_13/2,c_14/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,0#,prod#,sum#} and constructors {#,1,cons,nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {9}
        by application of
          Pre({9}) = {8}.
        Here rules are labelled as follows:
          1: *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
          2: *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
          3: +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
          4: +#(0(x),1(y)) -> c_7(+#(x,y))
          5: +#(1(x),0(y)) -> c_8(+#(x,y))
          6: +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
          7: prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
          8: sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
          9: sum#(nil()) -> c_14(0#(#()))
          10: *#(#(),x) -> c_1()
          11: +#(x,#()) -> c_4()
          12: +#(#(),x) -> c_5()
          13: 0#(#()) -> c_10()
          14: prod#(nil()) -> c_12()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_7(+#(x,y))
            +#(1(x),0(y)) -> c_8(+#(x,y))
            +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
        - Weak DPs:
            *#(#(),x) -> c_1()
            +#(x,#()) -> c_4()
            +#(#(),x) -> c_5()
            0#(#()) -> c_10()
            prod#(nil()) -> c_12()
            sum#(nil()) -> c_14(0#(#()))
        - Weak TRS:
            *(#(),x) -> #()
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,prod/1,sum/1,*#/2,+#/2,0#/1,prod#/1,sum#/1} / {#/0,1/1,cons/2,nil/0,c_1/0,c_2/2,c_3/3,c_4/0
            ,c_5/0,c_6/2,c_7/1,c_8/1,c_9/3,c_10/0,c_11/2,c_12/0,c_13/2,c_14/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,0#,prod#,sum#} and constructors {#,1,cons,nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
             -->_2 *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):2
             -->_1 0#(#()) -> c_10():12
             -->_2 *#(#(),x) -> c_1():9
             -->_2 *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y)):1
          
          2:S:*#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
             -->_2 0#(#()) -> c_10():12
             -->_1 +#(#(),x) -> c_5():11
             -->_1 +#(x,#()) -> c_4():10
             -->_3 *#(#(),x) -> c_1():9
             -->_3 *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):2
             -->_3 *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y)):1
          
          3:S:+#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
             -->_2 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_2 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_2 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 0#(#()) -> c_10():12
             -->_2 +#(#(),x) -> c_5():11
             -->_2 +#(x,#()) -> c_4():10
             -->_2 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          4:S:+#(0(x),1(y)) -> c_7(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(#(),x) -> c_5():11
             -->_1 +#(x,#()) -> c_4():10
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          5:S:+#(1(x),0(y)) -> c_8(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(#(),x) -> c_5():11
             -->_1 +#(x,#()) -> c_4():10
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          6:S:+#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
             -->_1 0#(#()) -> c_10():12
             -->_3 +#(#(),x) -> c_5():11
             -->_2 +#(#(),x) -> c_5():11
             -->_3 +#(x,#()) -> c_4():10
             -->_3 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_2 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_3 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_3 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_2 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_3 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          7:S:prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
             -->_2 prod#(nil()) -> c_12():13
             -->_1 *#(#(),x) -> c_1():9
             -->_2 prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l)):7
             -->_1 *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):2
             -->_1 *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y)):1
          
          8:S:sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
             -->_2 sum#(nil()) -> c_14(0#(#())):14
             -->_1 +#(#(),x) -> c_5():11
             -->_1 +#(x,#()) -> c_4():10
             -->_2 sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l)):8
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          9:W:*#(#(),x) -> c_1()
             
          
          10:W:+#(x,#()) -> c_4()
             
          
          11:W:+#(#(),x) -> c_5()
             
          
          12:W:0#(#()) -> c_10()
             
          
          13:W:prod#(nil()) -> c_12()
             
          
          14:W:sum#(nil()) -> c_14(0#(#()))
             -->_1 0#(#()) -> c_10():12
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          14: sum#(nil()) -> c_14(0#(#()))
          13: prod#(nil()) -> c_12()
          9: *#(#(),x) -> c_1()
          10: +#(x,#()) -> c_4()
          11: +#(#(),x) -> c_5()
          12: 0#(#()) -> c_10()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_7(+#(x,y))
            +#(1(x),0(y)) -> c_8(+#(x,y))
            +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
        - Weak TRS:
            *(#(),x) -> #()
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,prod/1,sum/1,*#/2,+#/2,0#/1,prod#/1,sum#/1} / {#/0,1/1,cons/2,nil/0,c_1/0,c_2/2,c_3/3,c_4/0
            ,c_5/0,c_6/2,c_7/1,c_8/1,c_9/3,c_10/0,c_11/2,c_12/0,c_13/2,c_14/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,0#,prod#,sum#} and constructors {#,1,cons,nil}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:*#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y))
             -->_2 *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):2
             -->_2 *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y)):1
          
          2:S:*#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
             -->_3 *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):2
             -->_3 *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y)):1
          
          3:S:+#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y))
             -->_2 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_2 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_2 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_2 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          4:S:+#(0(x),1(y)) -> c_7(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          5:S:+#(1(x),0(y)) -> c_8(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          6:S:+#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
             -->_3 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_2 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_3 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_3 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_2 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_3 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
          7:S:prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
             -->_2 prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l)):7
             -->_1 *#(1(x),y) -> c_3(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):2
             -->_1 *#(0(x),y) -> c_2(0#(*(x,y)),*#(x,y)):1
          
          8:S:sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
             -->_2 sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l)):8
             -->_1 +#(1(x),1(y)) -> c_9(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):6
             -->_1 +#(1(x),0(y)) -> c_8(+#(x,y)):5
             -->_1 +#(0(x),1(y)) -> c_7(+#(x,y)):4
             -->_1 +#(0(x),0(y)) -> c_6(0#(+(x,y)),+#(x,y)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          *#(0(x),y) -> c_2(*#(x,y))
          *#(1(x),y) -> c_3(+#(0(*(x,y)),y),*#(x,y))
          +#(0(x),0(y)) -> c_6(+#(x,y))
          +#(1(x),1(y)) -> c_9(+#(+(x,y),1(#())),+#(x,y))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(0(x),y) -> c_2(*#(x,y))
          *#(1(x),y) -> c_3(+#(0(*(x,y)),y),*#(x,y))
          +#(0(x),0(y)) -> c_6(+#(x,y))
          +#(0(x),1(y)) -> c_7(+#(x,y))
          +#(1(x),0(y)) -> c_8(+#(x,y))
          +#(1(x),1(y)) -> c_9(+#(+(x,y),1(#())),+#(x,y))
          prod#(cons(x,l)) -> c_11(*#(x,prod(l)),prod#(l))
          sum#(cons(x,l)) -> c_13(+#(x,sum(l)),sum#(l))
      - Weak TRS:
          *(#(),x) -> #()
          *(0(x),y) -> 0(*(x,y))
          *(1(x),y) -> +(0(*(x,y)),y)
          +(x,#()) -> x
          +(#(),x) -> x
          +(0(x),0(y)) -> 0(+(x,y))
          +(0(x),1(y)) -> 1(+(x,y))
          +(1(x),0(y)) -> 1(+(x,y))
          +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
          0(#()) -> #()
          prod(cons(x,l)) -> *(x,prod(l))
          prod(nil()) -> 1(#())
          sum(cons(x,l)) -> +(x,sum(l))
          sum(nil()) -> 0(#())
      - Signature:
          {*/2,+/2,0/1,prod/1,sum/1,*#/2,+#/2,0#/1,prod#/1,sum#/1} / {#/0,1/1,cons/2,nil/0,c_1/0,c_2/1,c_3/2,c_4/0
          ,c_5/0,c_6/1,c_7/1,c_8/1,c_9/2,c_10/0,c_11/2,c_12/0,c_13/2,c_14/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#,+#,0#,prod#,sum#} and constructors {#,1,cons,nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE