WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs)))
            duplicate(Nil()) -> Nil()
            goal(x) -> duplicate(x)
        - Signature:
            {duplicate/1,goal/1} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {duplicate,goal} 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:
          {duplicate,goal}
        TcT has computed the following interpretation:
               p(Cons) = [1] x2 + [0]
                p(Nil) = [0]         
          p(duplicate) = [1]         
               p(goal) = [5]         
        
        Following rules are strictly oriented:
        duplicate(Nil()) = [1]         
                         > [0]         
                         = Nil()       
        
                 goal(x) = [5]         
                         > [1]         
                         = duplicate(x)
        
        
        Following rules are (at-least) weakly oriented:
        duplicate(Cons(x,xs)) =  [1]                          
                              >= [1]                          
                              =  Cons(x,Cons(x,duplicate(xs)))
        
* Step 2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs)))
        - Weak TRS:
            duplicate(Nil()) -> Nil()
            goal(x) -> duplicate(x)
        - Signature:
            {duplicate/1,goal/1} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          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:
            all
          TcT has computed the following interpretation:
                 p(Cons) = [1] x2 + [4]
                  p(Nil) = [3]         
            p(duplicate) = [5] x1 + [2]
                 p(goal) = [5] x1 + [2]
          
          Following rules are strictly oriented:
          duplicate(Cons(x,xs)) = [5] xs + [22]                
                                > [5] xs + [10]                
                                = Cons(x,Cons(x,duplicate(xs)))
          
          
          Following rules are (at-least) weakly oriented:
          duplicate(Nil()) =  [17]        
                           >= [3]         
                           =  Nil()       
          
                   goal(x) =  [5] x + [2] 
                           >= [5] x + [2] 
                           =  duplicate(x)
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs)))
            duplicate(Nil()) -> Nil()
            goal(x) -> duplicate(x)
        - Signature:
            {duplicate/1,goal/1} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))