WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a,cons(x,k)) -> f(cons(x,a),k)
            f(a,empty()) -> g(a,empty())
            g(cons(x,k),d) -> g(k,cons(x,d))
            g(empty(),d) -> d
        - Signature:
            {f/2,g/2} / {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) = [1] x2 + [4]         
          p(empty) = [1]                  
              p(f) = [1] x1 + [4] x2 + [0]
              p(g) = [1] x1 + [1] x2 + [1]
        
        Following rules are strictly oriented:
        f(a,cons(x,k)) = [1] a + [4] k + [16]
                       > [1] a + [4] k + [4] 
                       = f(cons(x,a),k)      
        
          f(a,empty()) = [1] a + [4]         
                       > [1] a + [2]         
                       = g(a,empty())        
        
          g(empty(),d) = [1] d + [2]         
                       > [1] d + [0]         
                       = d                   
        
        
        Following rules are (at-least) weakly oriented:
        g(cons(x,k),d) =  [1] d + [1] k + [5]
                       >= [1] d + [1] k + [5]
                       =  g(k,cons(x,d))     
        
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(cons(x,k),d) -> g(k,cons(x,d))
        - Weak TRS:
            f(a,cons(x,k)) -> f(cons(x,a),k)
            f(a,empty()) -> g(a,empty())
            g(empty(),d) -> d
        - Signature:
            {f/2,g/2} / {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) = [1] x2 + [1]          
          p(empty) = [4]                   
              p(f) = [3] x1 + [4] x2 + [13]
              p(g) = [2] x1 + [1] x2 + [0] 
        
        Following rules are strictly oriented:
        g(cons(x,k),d) = [1] d + [2] k + [2]
                       > [1] d + [2] k + [1]
                       = g(k,cons(x,d))     
        
        
        Following rules are (at-least) weakly oriented:
        f(a,cons(x,k)) =  [3] a + [4] k + [17]
                       >= [3] a + [4] k + [16]
                       =  f(cons(x,a),k)      
        
          f(a,empty()) =  [3] a + [29]        
                       >= [2] a + [4]         
                       =  g(a,empty())        
        
          g(empty(),d) =  [1] d + [8]         
                       >= [1] d + [0]         
                       =  d                   
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(a,cons(x,k)) -> f(cons(x,a),k)
            f(a,empty()) -> g(a,empty())
            g(cons(x,k),d) -> g(k,cons(x,d))
            g(empty(),d) -> d
        - Signature:
            {f/2,g/2} / {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))