MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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()
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
          *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
          +#(x,#()) -> c_5()
          +#(#(),x) -> c_6()
          +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
          +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
          +#(0(x),1(y)) -> c_9(+#(x,y))
          +#(1(x),0(y)) -> c_10(+#(x,y))
          +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
          0#(#()) -> c_12()
          prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
          prod#(nil()) -> c_14()
          sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
          sum#(nil()) -> c_16(0#(#()))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(#(),x) -> c_1()
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(x,#()) -> c_5()
            +#(#(),x) -> c_6()
            +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
            +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_9(+#(x,y))
            +#(1(x),0(y)) -> c_10(+#(x,y))
            +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            0#(#()) -> c_12()
            prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
            prod#(nil()) -> c_14()
            sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
            sum#(nil()) -> c_16(0#(#()))
        - Weak TRS:
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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_3/2,c_4/3
            ,c_5/0,c_6/0,c_7/2,c_8/2,c_9/1,c_10/1,c_11/3,c_12/0,c_13/2,c_14/0,c_15/2,c_16/1}
        - 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
          {1,5,6,12,14}
        by application of
          Pre({1,5,6,12,14}) = {2,3,4,7,8,9,10,11,13,15,16}.
        Here rules are labelled as follows:
          1: *#(#(),x) -> c_1()
          2: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          3: *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
          4: *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
          5: +#(x,#()) -> c_5()
          6: +#(#(),x) -> c_6()
          7: +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
          8: +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
          9: +#(0(x),1(y)) -> c_9(+#(x,y))
          10: +#(1(x),0(y)) -> c_10(+#(x,y))
          11: +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
          12: 0#(#()) -> c_12()
          13: prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
          14: prod#(nil()) -> c_14()
          15: sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
          16: sum#(nil()) -> c_16(0#(#()))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
            +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_9(+#(x,y))
            +#(1(x),0(y)) -> c_10(+#(x,y))
            +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
            sum#(nil()) -> c_16(0#(#()))
        - Weak DPs:
            *#(#(),x) -> c_1()
            +#(x,#()) -> c_5()
            +#(#(),x) -> c_6()
            0#(#()) -> c_12()
            prod#(nil()) -> c_14()
        - Weak TRS:
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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_3/2,c_4/3
            ,c_5/0,c_6/0,c_7/2,c_8/2,c_9/1,c_10/1,c_11/3,c_12/0,c_13/2,c_14/0,c_15/2,c_16/1}
        - 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
          {11}
        by application of
          Pre({11}) = {10}.
        Here rules are labelled as follows:
          1: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          2: *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
          3: *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
          4: +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
          5: +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
          6: +#(0(x),1(y)) -> c_9(+#(x,y))
          7: +#(1(x),0(y)) -> c_10(+#(x,y))
          8: +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
          9: prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
          10: sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
          11: sum#(nil()) -> c_16(0#(#()))
          12: *#(#(),x) -> c_1()
          13: +#(x,#()) -> c_5()
          14: +#(#(),x) -> c_6()
          15: 0#(#()) -> c_12()
          16: prod#(nil()) -> c_14()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
            +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_9(+#(x,y))
            +#(1(x),0(y)) -> c_10(+#(x,y))
            +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
        - Weak DPs:
            *#(#(),x) -> c_1()
            +#(x,#()) -> c_5()
            +#(#(),x) -> c_6()
            0#(#()) -> c_12()
            prod#(nil()) -> c_14()
            sum#(nil()) -> c_16(0#(#()))
        - Weak TRS:
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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_3/2,c_4/3
            ,c_5/0,c_6/0,c_7/2,c_8/2,c_9/1,c_10/1,c_11/3,c_12/0,c_13/2,c_14/0,c_15/2,c_16/1}
        - 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:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_1 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_2 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_1 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_2 *#(#(),x) -> c_1():11
             -->_1 *#(#(),x) -> c_1():11
             -->_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:*#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
             -->_2 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_1 0#(#()) -> c_12():14
             -->_2 *#(#(),x) -> c_1():11
             -->_2 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          3:S:*#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
             -->_2 0#(#()) -> c_12():14
             -->_1 +#(#(),x) -> c_6():13
             -->_1 +#(x,#()) -> c_5():12
             -->_3 *#(#(),x) -> c_1():11
             -->_3 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_3 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_3 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          4:S:+#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
             -->_2 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_2 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_2 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_2 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_2 +#(#(),x) -> c_6():13
             -->_1 +#(#(),x) -> c_6():13
             -->_2 +#(x,#()) -> c_5():12
             -->_1 +#(x,#()) -> c_5():12
             -->_2 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          5:S:+#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
             -->_2 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_2 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_2 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 0#(#()) -> c_12():14
             -->_2 +#(#(),x) -> c_6():13
             -->_2 +#(x,#()) -> c_5():12
             -->_2 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_2 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          6:S:+#(0(x),1(y)) -> c_9(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(#(),x) -> c_6():13
             -->_1 +#(x,#()) -> c_5():12
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          7:S:+#(1(x),0(y)) -> c_10(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(#(),x) -> c_6():13
             -->_1 +#(x,#()) -> c_5():12
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          8:S:+#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
             -->_1 0#(#()) -> c_12():14
             -->_3 +#(#(),x) -> c_6():13
             -->_2 +#(#(),x) -> c_6():13
             -->_3 +#(x,#()) -> c_5():12
             -->_3 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_2 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_3 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_3 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_2 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_3 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_3 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
             -->_2 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          9:S:prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
             -->_2 prod#(nil()) -> c_14():15
             -->_1 *#(#(),x) -> c_1():11
             -->_2 prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l)):9
             -->_1 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_1 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          10:S:sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
             -->_2 sum#(nil()) -> c_16(0#(#())):16
             -->_1 +#(#(),x) -> c_6():13
             -->_1 +#(x,#()) -> c_5():12
             -->_2 sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l)):10
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          11:W:*#(#(),x) -> c_1()
             
          
          12:W:+#(x,#()) -> c_5()
             
          
          13:W:+#(#(),x) -> c_6()
             
          
          14:W:0#(#()) -> c_12()
             
          
          15:W:prod#(nil()) -> c_14()
             
          
          16:W:sum#(nil()) -> c_16(0#(#()))
             -->_1 0#(#()) -> c_12():14
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          16: sum#(nil()) -> c_16(0#(#()))
          15: prod#(nil()) -> c_14()
          11: *#(#(),x) -> c_1()
          12: +#(x,#()) -> c_5()
          13: +#(#(),x) -> c_6()
          14: 0#(#()) -> c_12()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
            *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
            +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
            +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
            +#(0(x),1(y)) -> c_9(+#(x,y))
            +#(1(x),0(y)) -> c_10(+#(x,y))
            +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
            prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
            sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
        - Weak TRS:
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(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_3/2,c_4/3
            ,c_5/0,c_6/0,c_7/2,c_8/2,c_9/1,c_10/1,c_11/3,c_12/0,c_13/2,c_14/0,c_15/2,c_16/1}
        - 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:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_1 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_2 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_1 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_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:*#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y))
             -->_2 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_2 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          3:S:*#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y))
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
             -->_3 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_3 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_3 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          4:S:+#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
             -->_2 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_2 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_2 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_2 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_2 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          5:S:+#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y))
             -->_2 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_2 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_2 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_2 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_2 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          6:S:+#(0(x),1(y)) -> c_9(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          7:S:+#(1(x),0(y)) -> c_10(+#(x,y))
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          8:S:+#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y))
             -->_3 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_2 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_3 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_3 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_2 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_3 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_3 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
             -->_2 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
          9:S:prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
             -->_2 prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l)):9
             -->_1 *#(1(x),y) -> c_4(+#(0(*(x,y)),y),0#(*(x,y)),*#(x,y)):3
             -->_1 *#(0(x),y) -> c_3(0#(*(x,y)),*#(x,y)):2
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          10:S:sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
             -->_2 sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l)):10
             -->_1 +#(1(x),1(y)) -> c_11(0#(+(+(x,y),1(#()))),+#(+(x,y),1(#())),+#(x,y)):8
             -->_1 +#(1(x),0(y)) -> c_10(+#(x,y)):7
             -->_1 +#(0(x),1(y)) -> c_9(+#(x,y)):6
             -->_1 +#(0(x),0(y)) -> c_8(0#(+(x,y)),+#(x,y)):5
             -->_1 +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z)):4
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          *#(0(x),y) -> c_3(*#(x,y))
          *#(1(x),y) -> c_4(+#(0(*(x,y)),y),*#(x,y))
          +#(0(x),0(y)) -> c_8(+#(x,y))
          +#(1(x),1(y)) -> c_11(+#(+(x,y),1(#())),+#(x,y))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(0(x),y) -> c_3(*#(x,y))
          *#(1(x),y) -> c_4(+#(0(*(x,y)),y),*#(x,y))
          +#(+(x,y),z) -> c_7(+#(x,+(y,z)),+#(y,z))
          +#(0(x),0(y)) -> c_8(+#(x,y))
          +#(0(x),1(y)) -> c_9(+#(x,y))
          +#(1(x),0(y)) -> c_10(+#(x,y))
          +#(1(x),1(y)) -> c_11(+#(+(x,y),1(#())),+#(x,y))
          prod#(cons(x,l)) -> c_13(*#(x,prod(l)),prod#(l))
          sum#(cons(x,l)) -> c_15(+#(x,sum(l)),sum#(l))
      - Weak TRS:
          *(#(),x) -> #()
          *(*(x,y),z) -> *(x,*(y,z))
          *(0(x),y) -> 0(*(x,y))
          *(1(x),y) -> +(0(*(x,y)),y)
          +(x,#()) -> x
          +(#(),x) -> x
          +(+(x,y),z) -> +(x,+(y,z))
          +(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_3/1,c_4/2
          ,c_5/0,c_6/0,c_7/2,c_8/1,c_9/1,c_10/1,c_11/2,c_12/0,c_13/2,c_14/0,c_15/2,c_16/1}
      - 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