WORST_CASE(?,O(n^1))
* Step 1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            main(x1) -> take_l#2(x1)
            take_l#2(0()) -> Nil()
            take_l#2(S(x2)) -> Cons(take_l#2(x2))
        - Signature:
            {main/1,take_l#2/1} / {0/0,Cons/1,Nil/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,take_l#2} and constructors {0,Cons,Nil,S}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(Cons) = {1}
        
        Following symbols are considered usable:
          {main,take_l#2}
        TcT has computed the following interpretation:
                 p(0) = 0 
              p(Cons) = x1
               p(Nil) = 0 
                 p(S) = 0 
              p(main) = 8 
          p(take_l#2) = 0 
        
        Following rules are strictly oriented:
        main(x1) = 8           
                 > 0           
                 = take_l#2(x1)
        
        
        Following rules are (at-least) weakly oriented:
          take_l#2(0()) =  0                 
                        >= 0                 
                        =  Nil()             
        
        take_l#2(S(x2)) =  0                 
                        >= 0                 
                        =  Cons(take_l#2(x2))
        
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            take_l#2(0()) -> Nil()
            take_l#2(S(x2)) -> Cons(take_l#2(x2))
        - Weak TRS:
            main(x1) -> take_l#2(x1)
        - Signature:
            {main/1,take_l#2/1} / {0/0,Cons/1,Nil/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,take_l#2} and constructors {0,Cons,Nil,S}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(Cons) = {1}
        
        Following symbols are considered usable:
          {main,take_l#2}
        TcT has computed the following interpretation:
                 p(0) = 0 
              p(Cons) = x1
               p(Nil) = 2 
                 p(S) = 0 
              p(main) = 4 
          p(take_l#2) = 4 
        
        Following rules are strictly oriented:
        take_l#2(0()) = 4    
                      > 2    
                      = Nil()
        
        
        Following rules are (at-least) weakly oriented:
               main(x1) =  4                 
                        >= 4                 
                        =  take_l#2(x1)      
        
        take_l#2(S(x2)) =  4                 
                        >= 4                 
                        =  Cons(take_l#2(x2))
        
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            take_l#2(S(x2)) -> Cons(take_l#2(x2))
        - Weak TRS:
            main(x1) -> take_l#2(x1)
            take_l#2(0()) -> Nil()
        - Signature:
            {main/1,take_l#2/1} / {0/0,Cons/1,Nil/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,take_l#2} and constructors {0,Cons,Nil,S}
    + 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) = {1}
        
        Following symbols are considered usable:
          {main,take_l#2}
        TcT has computed the following interpretation:
                 p(0) = [0]         
              p(Cons) = [1] x1 + [9]
               p(Nil) = [0]         
                 p(S) = [1] x1 + [2]
              p(main) = [5] x1 + [0]
          p(take_l#2) = [5] x1 + [0]
        
        Following rules are strictly oriented:
        take_l#2(S(x2)) = [5] x2 + [10]     
                        > [5] x2 + [9]      
                        = Cons(take_l#2(x2))
        
        
        Following rules are (at-least) weakly oriented:
             main(x1) =  [5] x1 + [0]
                      >= [5] x1 + [0]
                      =  take_l#2(x1)
        
        take_l#2(0()) =  [0]         
                      >= [0]         
                      =  Nil()       
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            main(x1) -> take_l#2(x1)
            take_l#2(0()) -> Nil()
            take_l#2(S(x2)) -> Cons(take_l#2(x2))
        - Signature:
            {main/1,take_l#2/1} / {0/0,Cons/1,Nil/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,take_l#2} and constructors {0,Cons,Nil,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))