MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(),x) -> 0()
            *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
            +(x,0()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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()
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(0(),x) -> c_3()
          *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y))
          +#(x,0()) -> c_5()
          +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z))
          +#(0(),x) -> c_7()
          +#(s(x),s(y)) -> c_8(+#(x,y))
          prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l))
          prod#(nil()) -> c_10()
          sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l))
          sum#(nil()) -> c_12()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(0(),x) -> c_3()
            *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y))
            +#(x,0()) -> c_5()
            +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z))
            +#(0(),x) -> c_7()
            +#(s(x),s(y)) -> c_8(+#(x,y))
            prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l))
            prod#(nil()) -> c_10()
            sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l))
            sum#(nil()) -> c_12()
        - Weak TRS:
            *(x,0()) -> 0()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(),x) -> 0()
            *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
            +(x,0()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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_2/2,c_3/0,c_4/3,c_5/0,c_6/2
            ,c_7/0,c_8/1,c_9/2,c_10/0,c_11/2,c_12/0}
        - 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
          {1,3,5,7,10,12}
        by application of
          Pre({1,3,5,7,10,12}) = {2,4,6,8,9,11}.
        Here rules are labelled as follows:
          1: *#(x,0()) -> c_1()
          2: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          3: *#(0(),x) -> c_3()
          4: *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y))
          5: +#(x,0()) -> c_5()
          6: +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z))
          7: +#(0(),x) -> c_7()
          8: +#(s(x),s(y)) -> c_8(+#(x,y))
          9: prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l))
          10: prod#(nil()) -> c_10()
          11: sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l))
          12: sum#(nil()) -> c_12()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y))
            +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z))
            +#(s(x),s(y)) -> c_8(+#(x,y))
            prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l))
        - Weak DPs:
            *#(x,0()) -> c_1()
            *#(0(),x) -> c_3()
            +#(x,0()) -> c_5()
            +#(0(),x) -> c_7()
            prod#(nil()) -> c_10()
            sum#(nil()) -> c_12()
        - Weak TRS:
            *(x,0()) -> 0()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(),x) -> 0()
            *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
            +(x,0()) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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_2/2,c_3/0,c_4/3,c_5/0,c_6/2
            ,c_7/0,c_8/1,c_9/2,c_10/0,c_11/2,c_12/0}
        - 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:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y)):2
             -->_1 *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y)):2
             -->_2 *#(0(),x) -> c_3():8
             -->_1 *#(0(),x) -> c_3():8
             -->_2 *#(x,0()) -> c_1():7
             -->_1 *#(x,0()) -> c_1():7
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          2:S:*#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y))
             -->_3 +#(s(x),s(y)) -> c_8(+#(x,y)):4
             -->_1 +#(s(x),s(y)) -> c_8(+#(x,y)):4
             -->_3 +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z)):3
             -->_1 +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z)):3
             -->_3 +#(0(),x) -> c_7():10
             -->_1 +#(0(),x) -> c_7():10
             -->_3 +#(x,0()) -> c_5():9
             -->_1 +#(x,0()) -> c_5():9
             -->_2 *#(0(),x) -> c_3():8
             -->_2 *#(x,0()) -> c_1():7
             -->_2 *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          3:S:+#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z))
             -->_2 +#(s(x),s(y)) -> c_8(+#(x,y)):4
             -->_1 +#(s(x),s(y)) -> c_8(+#(x,y)):4
             -->_2 +#(0(),x) -> c_7():10
             -->_1 +#(0(),x) -> c_7():10
             -->_2 +#(x,0()) -> c_5():9
             -->_1 +#(x,0()) -> c_5():9
             -->_2 +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z)):3
             -->_1 +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z)):3
          
          4:S:+#(s(x),s(y)) -> c_8(+#(x,y))
             -->_1 +#(0(),x) -> c_7():10
             -->_1 +#(x,0()) -> c_5():9
             -->_1 +#(s(x),s(y)) -> c_8(+#(x,y)):4
             -->_1 +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z)):3
          
          5:S:prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l))
             -->_2 prod#(nil()) -> c_10():11
             -->_1 *#(0(),x) -> c_3():8
             -->_1 *#(x,0()) -> c_1():7
             -->_2 prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l)):5
             -->_1 *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y)):2
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          6:S:sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l))
             -->_2 sum#(nil()) -> c_12():12
             -->_1 +#(0(),x) -> c_7():10
             -->_1 +#(x,0()) -> c_5():9
             -->_2 sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l)):6
             -->_1 +#(s(x),s(y)) -> c_8(+#(x,y)):4
             -->_1 +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z)):3
          
          7:W:*#(x,0()) -> c_1()
             
          
          8:W:*#(0(),x) -> c_3()
             
          
          9:W:+#(x,0()) -> c_5()
             
          
          10:W:+#(0(),x) -> c_7()
             
          
          11:W:prod#(nil()) -> c_10()
             
          
          12:W:sum#(nil()) -> c_12()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: sum#(nil()) -> c_12()
          11: prod#(nil()) -> c_10()
          7: *#(x,0()) -> c_1()
          8: *#(0(),x) -> c_3()
          9: +#(x,0()) -> c_5()
          10: +#(0(),x) -> c_7()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(s(x),s(y)) -> c_4(+#(*(x,y),+(x,y)),*#(x,y),+#(x,y))
          +#(+(x,y),z) -> c_6(+#(x,+(y,z)),+#(y,z))
          +#(s(x),s(y)) -> c_8(+#(x,y))
          prod#(cons(x,l)) -> c_9(*#(x,prod(l)),prod#(l))
          sum#(cons(x,l)) -> c_11(+#(x,sum(l)),sum#(l))
      - Weak TRS:
          *(x,0()) -> 0()
          *(*(x,y),z) -> *(x,*(y,z))
          *(0(),x) -> 0()
          *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
          +(x,0()) -> x
          +(+(x,y),z) -> +(x,+(y,z))
          +(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_2/2,c_3/0,c_4/3,c_5/0,c_6/2
          ,c_7/0,c_8/1,c_9/2,c_10/0,c_11/2,c_12/0}
      - 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