WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(0()) -> cons(0(),f(s(0())))
            a__f(s(0())) -> a__f(a__p(s(0())))
            a__p(X) -> p(X)
            a__p(s(0())) -> 0()
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(f(X)) -> a__f(mark(X))
            mark(p(X)) -> a__p(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,a__p,mark} and constructors {0,cons,f,p,s}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(a__f) = {1},
          uargs(a__p) = {1},
          uargs(cons) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {a__f,a__p,mark}
        TcT has computed the following interpretation:
             p(0) = [0]           
                    [0]           
          p(a__f) = [1 4] x1 + [2]
                    [0 0]      [2]
          p(a__p) = [1 1] x1 + [4]
                    [0 0]      [1]
          p(cons) = [1 3] x1 + [0]
                    [0 0]      [2]
             p(f) = [1 2] x1 + [0]
                    [0 0]      [2]
          p(mark) = [4 2] x1 + [5]
                    [0 1]      [0]
             p(p) = [1 1] x1 + [2]
                    [0 0]      [1]
             p(s) = [1 2] x1 + [1]
                    [0 0]      [3]
        
        Following rules are strictly oriented:
                  a__f(X) = [1 4] X + [2]      
                            [0 0]     [2]      
                          > [1 2] X + [0]      
                            [0 0]     [2]      
                          = f(X)               
        
                a__f(0()) = [2]                
                            [2]                
                          > [0]                
                            [2]                
                          = cons(0(),f(s(0())))
        
             a__f(s(0())) = [15]               
                            [2]                
                          > [14]               
                            [2]                
                          = a__f(a__p(s(0()))) 
        
                  a__p(X) = [1 1] X + [4]      
                            [0 0]     [1]      
                          > [1 1] X + [2]      
                            [0 0]     [1]      
                          = p(X)               
        
             a__p(s(0())) = [8]                
                            [1]                
                          > [0]                
                            [0]                
                          = 0()                
        
                mark(0()) = [5]                
                            [0]                
                          > [0]                
                            [0]                
                          = 0()                
        
        mark(cons(X1,X2)) = [4 12] X1 + [9]    
                            [0  0]      [2]    
                          > [4 5] X1 + [5]     
                            [0 0]      [2]     
                          = cons(mark(X1),X2)  
        
               mark(f(X)) = [4 8] X + [9]      
                            [0 0]     [2]      
                          > [4 6] X + [7]      
                            [0 0]     [2]      
                          = a__f(mark(X))      
        
               mark(p(X)) = [4 4] X + [15]     
                            [0 0]     [1]      
                          > [4 3] X + [9]      
                            [0 0]     [1]      
                          = a__p(mark(X))      
        
               mark(s(X)) = [4 8] X + [15]     
                            [0 0]     [3]      
                          > [4 4] X + [6]      
                            [0 0]     [3]      
                          = s(mark(X))         
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))