WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(cons(x,k),l) -> g(k,l,cons(x,k))
            f(empty(),l) -> l
            g(a,b,c) -> f(a,cons(b,c))
        - Signature:
            {f/2,g/3} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
    + 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:
          none
        
        Following symbols are considered usable:
          {f,g}
        TcT has computed the following interpretation:
           p(cons) = [0]          
          p(empty) = [0]          
              p(f) = [2] x2 + [11]
              p(g) = [11]         
        
        Following rules are strictly oriented:
        f(empty(),l) = [2] l + [11]
                     > [1] l + [0] 
                     = l           
        
        
        Following rules are (at-least) weakly oriented:
        f(cons(x,k),l) =  [2] l + [11]    
                       >= [11]            
                       =  g(k,l,cons(x,k))
        
              g(a,b,c) =  [11]            
                       >= [11]            
                       =  f(a,cons(b,c))  
        
* Step 2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(cons(x,k),l) -> g(k,l,cons(x,k))
            g(a,b,c) -> f(a,cons(b,c))
        - Weak TRS:
            f(empty(),l) -> l
        - Signature:
            {f/2,g/3} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
    + 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:
            none
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
             p(cons) = [1] x1 + [0]
            p(empty) = [0]         
                p(f) = [3] x2 + [0]
                p(g) = [3] x2 + [1]
          
          Following rules are strictly oriented:
          g(a,b,c) = [3] b + [1]   
                   > [3] b + [0]   
                   = f(a,cons(b,c))
          
          
          Following rules are (at-least) weakly oriented:
          f(cons(x,k),l) =  [3] l + [0]     
                         >= [3] l + [1]     
                         =  g(k,l,cons(x,k))
          
            f(empty(),l) =  [3] l + [0]     
                         >= [1] l + [0]     
                         =  l               
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(cons(x,k),l) -> g(k,l,cons(x,k))
        - Weak TRS:
            f(empty(),l) -> l
            g(a,b,c) -> f(a,cons(b,c))
        - Signature:
            {f/2,g/3} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 1, araTimeout = 15, araFindStrictRules = Just 1}
    + Details:
        Signatures used:
        ----------------
          cons :: [A(0) x A(13)] -(13)-> A(13)
          cons :: [A(0) x A(0)] -(0)-> A(0)
          empty :: [] -(0)-> A(13)
          f :: [A(13) x A(0)] -(15)-> A(0)
          g :: [A(13) x A(0) x A(0)] -(15)-> A(0)
        
        
        Cost-free Signatures used:
        --------------------------
          cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          empty :: [] -(0)-> A_cf(0)
          f :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          g :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          cons_A :: [A(0) x A(1)] -(1)-> A(1)
          empty_A :: [] -(0)-> A(1)
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(cons(x,k),l) -> g(k,l,cons(x,k))
        2. Weak:
          
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(cons(x,k),l) -> g(k,l,cons(x,k))
            f(empty(),l) -> l
            g(a,b,c) -> f(a,cons(b,c))
        - Signature:
            {f/2,g/3} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))