WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            append(cons(x,xs),ys) -> cons(x,append(xs,ys))
            append(nil(),ys) -> ys
            main(xs) -> append(xs,nil())
        - Signature:
            {append/2,main/1} / {cons/2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,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}
        
        Following symbols are considered usable:
          {append,main}
        TcT has computed the following interpretation:
          p(append) = [2] x2 + [1]
            p(cons) = [1] x2 + [0]
            p(main) = [4] x1 + [1]
             p(nil) = [0]         
        
        Following rules are strictly oriented:
        append(nil(),ys) = [2] ys + [1]
                         > [1] ys + [0]
                         = ys          
        
        
        Following rules are (at-least) weakly oriented:
        append(cons(x,xs),ys) =  [2] ys + [1]         
                              >= [2] ys + [1]         
                              =  cons(x,append(xs,ys))
        
                     main(xs) =  [4] xs + [1]         
                              >= [1]                  
                              =  append(xs,nil())     
        
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            append(cons(x,xs),ys) -> cons(x,append(xs,ys))
            main(xs) -> append(xs,nil())
        - Weak TRS:
            append(nil(),ys) -> ys
        - Signature:
            {append/2,main/1} / {cons/2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,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}
        
        Following symbols are considered usable:
          {append,main}
        TcT has computed the following interpretation:
          p(append) = [3] x1 + [2] x2 + [0]
            p(cons) = [1] x2 + [8]         
            p(main) = [3] x1 + [1]         
             p(nil) = [0]                  
        
        Following rules are strictly oriented:
        append(cons(x,xs),ys) = [3] xs + [2] ys + [24]
                              > [3] xs + [2] ys + [8] 
                              = cons(x,append(xs,ys)) 
        
                     main(xs) = [3] xs + [1]          
                              > [3] xs + [0]          
                              = append(xs,nil())      
        
        
        Following rules are (at-least) weakly oriented:
        append(nil(),ys) =  [2] ys + [0]
                         >= [1] ys + [0]
                         =  ys          
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            append(cons(x,xs),ys) -> cons(x,append(xs,ys))
            append(nil(),ys) -> ys
            main(xs) -> append(xs,nil())
        - Signature:
            {append/2,main/1} / {cons/2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {append,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))