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