WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            app_xs#1(Cons(x7,x8),x10) -> Cons(x7,app_xs#1(x8,x10))
            app_xs#1(Nil(),x6) -> x6
            main(x4,x2) -> app_xs#1(x4,app_xs#1(x4,x2))
        - Signature:
            {app_xs#1/2,main/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app_xs#1,main} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(Cons) = {2},
          uargs(app_xs#1) = {2}
        
        Following symbols are considered usable:
          {app_xs#1,main}
        TcT has computed the following interpretation:
              p(Cons) = [1] x1 + [1] x2 + [1] 
               p(Nil) = [4]                   
          p(app_xs#1) = [2] x1 + [2] x2 + [4] 
              p(main) = [7] x1 + [4] x2 + [12]
        
        Following rules are strictly oriented:
        app_xs#1(Cons(x7,x8),x10) = [2] x10 + [2] x7 + [2] x8 + [6]
                                  > [2] x10 + [1] x7 + [2] x8 + [5]
                                  = Cons(x7,app_xs#1(x8,x10))      
        
               app_xs#1(Nil(),x6) = [2] x6 + [12]                  
                                  > [1] x6 + [0]                   
                                  = x6                             
        
        
        Following rules are (at-least) weakly oriented:
        main(x4,x2) =  [4] x2 + [7] x4 + [12]      
                    >= [4] x2 + [6] x4 + [12]      
                    =  app_xs#1(x4,app_xs#1(x4,x2))
        
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            main(x4,x2) -> app_xs#1(x4,app_xs#1(x4,x2))
        - Weak TRS:
            app_xs#1(Cons(x7,x8),x10) -> Cons(x7,app_xs#1(x8,x10))
            app_xs#1(Nil(),x6) -> x6
        - Signature:
            {app_xs#1/2,main/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app_xs#1,main} and constructors {Cons,Nil}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(Cons) = {2},
          uargs(app_xs#1) = {2}
        
        Following symbols are considered usable:
          {app_xs#1,main}
        TcT has computed the following interpretation:
              p(Cons) = [1] x1 + [1] x2 + [0]
               p(Nil) = [6]                  
          p(app_xs#1) = [1] x1 + [1] x2 + [0]
              p(main) = [8] x1 + [1] x2 + [9]
        
        Following rules are strictly oriented:
        main(x4,x2) = [1] x2 + [8] x4 + [9]       
                    > [1] x2 + [2] x4 + [0]       
                    = app_xs#1(x4,app_xs#1(x4,x2))
        
        
        Following rules are (at-least) weakly oriented:
        app_xs#1(Cons(x7,x8),x10) =  [1] x10 + [1] x7 + [1] x8 + [0]
                                  >= [1] x10 + [1] x7 + [1] x8 + [0]
                                  =  Cons(x7,app_xs#1(x8,x10))      
        
               app_xs#1(Nil(),x6) =  [1] x6 + [6]                   
                                  >= [1] x6 + [0]                   
                                  =  x6                             
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            app_xs#1(Cons(x7,x8),x10) -> Cons(x7,app_xs#1(x8,x10))
            app_xs#1(Nil(),x6) -> x6
            main(x4,x2) -> app_xs#1(x4,app_xs#1(x4,x2))
        - Signature:
            {app_xs#1/2,main/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app_xs#1,main} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))