MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          add0#(x,Nil()) -> c_1()
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          goal#(x,y) -> c_3(power#(x,y))
          mult#(x,Nil()) -> c_4()
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          power#(x,Nil()) -> c_6()
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x,Nil()) -> c_1()
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x,Nil()) -> c_4()
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x,Nil()) -> c_6()
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            goal(x,y) -> power(x,y)
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          add0(x,Nil()) -> x
          add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
          mult(x,Nil()) -> Nil()
          mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
          power(x,Nil()) -> Cons(Nil(),Nil())
          power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          add0#(x,Nil()) -> c_1()
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          goal#(x,y) -> c_3(power#(x,y))
          mult#(x,Nil()) -> c_4()
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          power#(x,Nil()) -> c_6()
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x,Nil()) -> c_1()
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x,Nil()) -> c_4()
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x,Nil()) -> c_6()
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,6}
        by application of
          Pre({1,4,6}) = {2,3,5,7}.
        Here rules are labelled as follows:
          1: add0#(x,Nil()) -> c_1()
          2: add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          3: goal#(x,y) -> c_3(power#(x,y))
          4: mult#(x,Nil()) -> c_4()
          5: mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          6: power#(x,Nil()) -> c_6()
          7: power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak DPs:
            add0#(x,Nil()) -> c_1()
            mult#(x,Nil()) -> c_4()
            power#(x,Nil()) -> c_6()
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
             -->_1 add0#(x,Nil()) -> c_1():5
             -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
          
          2:S:goal#(x,y) -> c_3(power#(x,y))
             -->_1 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
             -->_1 power#(x,Nil()) -> c_6():7
          
          3:S:mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
             -->_2 mult#(x,Nil()) -> c_4():6
             -->_1 add0#(x,Nil()) -> c_1():5
             -->_2 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
             -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
          
          4:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x,Nil()) -> c_6():7
             -->_1 mult#(x,Nil()) -> c_4():6
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
             -->_1 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
          
          5:W:add0#(x,Nil()) -> c_1()
             
          
          6:W:mult#(x,Nil()) -> c_4()
             
          
          7:W:power#(x,Nil()) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: mult#(x,Nil()) -> c_4()
          7: power#(x,Nil()) -> c_6()
          5: add0#(x,Nil()) -> c_1()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            goal#(x,y) -> c_3(power#(x,y))
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
           -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
        
        2:S:goal#(x,y) -> c_3(power#(x,y))
           -->_1 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
        
        3:S:mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
           -->_2 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
           -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):1
        
        4:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
           -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):4
           -->_1 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):3
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(2,goal#(x,y) -> c_3(power#(x,y)))]
* Step 6: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          - Weak DPs:
              mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
              power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
          - Weak TRS:
              add0(x,Nil()) -> x
              add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
              mult(x,Nil()) -> Nil()
              mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
              power(x,Nil()) -> Cons(Nil(),Nil())
              power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          - Signature:
              {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
              ,c_5/2,c_6/0,c_7/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
        
        Problem (S)
          - Strict DPs:
              mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
              power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
          - Weak DPs:
              add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          - Weak TRS:
              add0(x,Nil()) -> x
              add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
              mult(x,Nil()) -> Nil()
              mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
              power(x,Nil()) -> Cons(Nil(),Nil())
              power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          - Signature:
              {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
              ,c_5/2,c_6/0,c_7/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
** Step 6.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
        - Weak DPs:
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        and a lower component
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
        Further, following extension rules are added to the lower component.
          power#(x',Cons(x,xs)) -> mult#(x',power(x',xs))
          power#(x',Cons(x,xs)) -> power#(x',xs)
*** Step 6.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
          
        The strictly oriented rules are moved into the weak component.
**** Step 6.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_7) = {1,2}
        
        Following symbols are considered usable:
          {add0#,goal#,mult#,power#}
        TcT has computed the following interpretation:
            p(Cons) = [1] x2 + [8]         
             p(Nil) = [0]                  
            p(add0) = [1] x1 + [0]         
            p(goal) = [0]                  
            p(mult) = [8] x1 + [1]         
           p(power) = [1] x1 + [0]         
           p(add0#) = [1] x1 + [2] x2 + [0]
           p(goal#) = [1]                  
           p(mult#) = [0]                  
          p(power#) = [1] x2 + [0]         
             p(c_1) = [1]                  
             p(c_2) = [2] x1 + [1]         
             p(c_3) = [0]                  
             p(c_4) = [0]                  
             p(c_5) = [1] x1 + [1]         
             p(c_6) = [0]                  
             p(c_7) = [4] x1 + [1] x2 + [0]
        
        Following rules are strictly oriented:
        power#(x',Cons(x,xs)) = [1] xs + [8]                             
                              > [1] xs + [0]                             
                              = c_7(mult#(x',power(x',xs)),power#(x',xs))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 6.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 6.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
**** Step 6.a:1.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 6.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
      - Weak DPs:
          mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
          power#(x',Cons(x,xs)) -> mult#(x',power(x',xs))
          power#(x',Cons(x,xs)) -> power#(x',xs)
      - Weak TRS:
          add0(x,Nil()) -> x
          add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
          mult(x,Nil()) -> Nil()
          mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
          power(x,Nil()) -> Cons(Nil(),Nil())
          power(x',Cons(x,xs)) -> mult(x',power(x',xs))
      - Signature:
          {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
          ,c_5/2,c_6/0,c_7/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 6.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak DPs:
            add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
             -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):3
             -->_2 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):1
          
          2:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):2
             -->_1 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):1
          
          3:W:add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
             -->_1 add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs)):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: add0#(x',Cons(x,xs)) -> c_2(add0#(x',xs))
** Step 6.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/2,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs))
             -->_2 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):1
          
          2:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):2
             -->_1 mult#(x',Cons(x,xs)) -> c_5(add0#(x',mult(x',xs)),mult#(x',xs)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
** Step 6.b:3: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
          - Weak DPs:
              power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
          - Weak TRS:
              add0(x,Nil()) -> x
              add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
              mult(x,Nil()) -> Nil()
              mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
              power(x,Nil()) -> Cons(Nil(),Nil())
              power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          - Signature:
              {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
              ,c_5/1,c_6/0,c_7/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
        
        Problem (S)
          - Strict DPs:
              power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
          - Weak DPs:
              mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
          - Weak TRS:
              add0(x,Nil()) -> x
              add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
              mult(x,Nil()) -> Nil()
              mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
              power(x,Nil()) -> Cons(Nil(),Nil())
              power(x',Cons(x,xs)) -> mult(x',power(x',xs))
          - Signature:
              {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
              ,c_5/1,c_6/0,c_7/2}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
*** Step 6.b:3.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        and a lower component
          mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
        Further, following extension rules are added to the lower component.
          power#(x',Cons(x,xs)) -> mult#(x',power(x',xs))
          power#(x',Cons(x,xs)) -> power#(x',xs)
**** Step 6.b:3.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
          
        The strictly oriented rules are moved into the weak component.
***** Step 6.b:3.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_7) = {1,2}
        
        Following symbols are considered usable:
          {add0#,goal#,mult#,power#}
        TcT has computed the following interpretation:
            p(Cons) = [1] x2 + [5]         
             p(Nil) = [1]                  
            p(add0) = [8] x1 + [4]         
            p(goal) = [2]                  
            p(mult) = [4]                  
           p(power) = [0]                  
           p(add0#) = [4] x2 + [2]         
           p(goal#) = [8] x2 + [2]         
           p(mult#) = [8]                  
          p(power#) = [5] x2 + [6]         
             p(c_1) = [8]                  
             p(c_2) = [1] x1 + [0]         
             p(c_3) = [1] x1 + [2]         
             p(c_4) = [1]                  
             p(c_5) = [2] x1 + [1]         
             p(c_6) = [2]                  
             p(c_7) = [1] x1 + [1] x2 + [7]
        
        Following rules are strictly oriented:
        power#(x',Cons(x,xs)) = [5] xs + [31]                            
                              > [5] xs + [21]                            
                              = c_7(mult#(x',power(x',xs)),power#(x',xs))
        
        
        Following rules are (at-least) weakly oriented:
        
***** Step 6.b:3.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

***** Step 6.b:3.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
***** Step 6.b:3.a:1.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

**** Step 6.b:3.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
      - Weak DPs:
          power#(x',Cons(x,xs)) -> mult#(x',power(x',xs))
          power#(x',Cons(x,xs)) -> power#(x',xs)
      - Weak TRS:
          add0(x,Nil()) -> x
          add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
          mult(x,Nil()) -> Nil()
          mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
          power(x,Nil()) -> Cons(Nil(),Nil())
          power(x',Cons(x,xs)) -> mult(x',power(x',xs))
      - Signature:
          {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
          ,c_5/1,c_6/0,c_7/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
*** Step 6.b:3.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak DPs:
            mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_1 mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs)):2
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):1
          
          2:W:mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
             -->_1 mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: mult#(x',Cons(x,xs)) -> c_5(mult#(x',xs))
*** Step 6.b:3.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs))
             -->_2 power#(x',Cons(x,xs)) -> c_7(mult#(x',power(x',xs)),power#(x',xs)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
*** Step 6.b:3.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
        - Weak TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
            mult(x,Nil()) -> Nil()
            mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
            power(x,Nil()) -> Cons(Nil(),Nil())
            power(x',Cons(x,xs)) -> mult(x',power(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
*** Step 6.b:3.b:4: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
          
        The strictly oriented rules are moved into the weak component.
**** Step 6.b:3.b:4.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_7) = {1}
        
        Following symbols are considered usable:
          {add0#,goal#,mult#,power#}
        TcT has computed the following interpretation:
            p(Cons) = [1] x1 + [1] x2 + [4]
             p(Nil) = [0]                  
            p(add0) = [0]                  
            p(goal) = [1] x1 + [1] x2 + [0]
            p(mult) = [1] x1 + [1] x2 + [0]
           p(power) = [1] x1 + [2] x2 + [1]
           p(add0#) = [1] x2 + [8]         
           p(goal#) = [2] x1 + [2] x2 + [8]
           p(mult#) = [2] x1 + [1]         
          p(power#) = [4] x2 + [0]         
             p(c_1) = [1]                  
             p(c_2) = [1]                  
             p(c_3) = [1]                  
             p(c_4) = [4]                  
             p(c_5) = [1] x1 + [1]         
             p(c_6) = [1]                  
             p(c_7) = [1] x1 + [14]        
        
        Following rules are strictly oriented:
        power#(x',Cons(x,xs)) = [4] x + [4] xs + [16]
                              > [4] xs + [14]        
                              = c_7(power#(x',xs))   
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 6.b:3.b:4.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 6.b:3.b:4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
             -->_1 power#(x',Cons(x,xs)) -> c_7(power#(x',xs)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: power#(x',Cons(x,xs)) -> c_7(power#(x',xs))
**** Step 6.b:3.b:4.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {add0/2,goal/2,mult/2,power/2,add0#/2,goal#/2,mult#/2,power#/2} / {Cons/2,Nil/0,c_1/0,c_2/1,c_3/1,c_4/0
            ,c_5/1,c_6/0,c_7/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,mult#,power#} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

MAYBE