WORST_CASE(?,O(n^2))
* Step 1: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(add(X,Y))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__fst(X1,X2) -> fst(X1,X2)
            a__fst(0(),Z) -> nil()
            a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
            a__len(X) -> len(X)
            a__len(cons(X,Z)) -> s(len(Z))
            a__len(nil()) -> 0()
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
            mark(len(X)) -> a__len(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
        - Signature:
            {a__add/2,a__from/1,a__fst/2,a__len/1,mark/1} / {0/0,add/2,cons/2,from/1,fst/2,len/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__add,a__from,a__fst,a__len,mark} and constructors {0
            ,add,cons,from,fst,len,nil,s}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(a__add) = {1,2},
          uargs(a__from) = {1},
          uargs(a__fst) = {1,2},
          uargs(a__len) = {1},
          uargs(cons) = {1}
        
        Following symbols are considered usable:
          {a__add,a__from,a__fst,a__len,mark}
        TcT has computed the following interpretation:
                p(0) = [0]                      
                       [4]                      
           p(a__add) = [1 0] x1 + [1 1] x2 + [1]
                       [0 1]      [0 1]      [2]
          p(a__from) = [1 1] x1 + [1]           
                       [0 1]      [3]           
           p(a__fst) = [1 1] x1 + [1 1] x2 + [1]
                       [0 1]      [0 1]      [2]
           p(a__len) = [1 3] x1 + [3]           
                       [0 1]      [3]           
              p(add) = [1 0] x1 + [1 1] x2 + [0]
                       [0 1]      [0 1]      [2]
             p(cons) = [1 0] x1 + [0]           
                       [0 1]      [2]           
             p(from) = [1 1] x1 + [0]           
                       [0 1]      [3]           
              p(fst) = [1 1] x1 + [1 1] x2 + [0]
                       [0 1]      [0 1]      [2]
              p(len) = [1 3] x1 + [2]           
                       [0 1]      [3]           
             p(mark) = [1 1] x1 + [0]           
                       [0 1]      [0]           
              p(nil) = [0]                      
                       [4]                      
                p(s) = [4]                      
                       [4]                      
        
        Following rules are strictly oriented:
                 a__add(X1,X2) = [1 0] X1 + [1 1] X2 + [1]
                                 [0 1]      [0 1]      [2]
                               > [1 0] X1 + [1 1] X2 + [0]
                                 [0 1]      [0 1]      [2]
                               = add(X1,X2)               
        
                 a__add(0(),X) = [1 1] X + [1]            
                                 [0 1]     [6]            
                               > [1 1] X + [0]            
                                 [0 1]     [0]            
                               = mark(X)                  
        
                a__add(s(X),Y) = [1 1] Y + [5]            
                                 [0 1]     [6]            
                               > [4]                      
                                 [4]                      
                               = s(add(X,Y))              
        
                    a__from(X) = [1 1] X + [1]            
                                 [0 1]     [3]            
                               > [1 1] X + [0]            
                                 [0 1]     [2]            
                               = cons(mark(X),from(s(X))) 
        
                    a__from(X) = [1 1] X + [1]            
                                 [0 1]     [3]            
                               > [1 1] X + [0]            
                                 [0 1]     [3]            
                               = from(X)                  
        
                 a__fst(X1,X2) = [1 1] X1 + [1 1] X2 + [1]
                                 [0 1]      [0 1]      [2]
                               > [1 1] X1 + [1 1] X2 + [0]
                                 [0 1]      [0 1]      [2]
                               = fst(X1,X2)               
        
                 a__fst(0(),Z) = [1 1] Z + [5]            
                                 [0 1]     [6]            
                               > [0]                      
                                 [4]                      
                               = nil()                    
        
        a__fst(s(X),cons(Y,Z)) = [1 1] Y + [11]           
                                 [0 1]     [8]            
                               > [1 1] Y + [0]            
                                 [0 1]     [2]            
                               = cons(mark(Y),fst(X,Z))   
        
                     a__len(X) = [1 3] X + [3]            
                                 [0 1]     [3]            
                               > [1 3] X + [2]            
                                 [0 1]     [3]            
                               = len(X)                   
        
             a__len(cons(X,Z)) = [1 3] X + [9]            
                                 [0 1]     [5]            
                               > [4]                      
                                 [4]                      
                               = s(len(Z))                
        
                 a__len(nil()) = [15]                     
                                 [7]                      
                               > [0]                      
                                 [4]                      
                               = 0()                      
        
                     mark(0()) = [4]                      
                                 [4]                      
                               > [0]                      
                                 [4]                      
                               = 0()                      
        
              mark(add(X1,X2)) = [1 1] X1 + [1 2] X2 + [2]
                                 [0 1]      [0 1]      [2]
                               > [1 1] X1 + [1 2] X2 + [1]
                                 [0 1]      [0 1]      [2]
                               = a__add(mark(X1),mark(X2))
        
             mark(cons(X1,X2)) = [1 1] X1 + [2]           
                                 [0 1]      [2]           
                               > [1 1] X1 + [0]           
                                 [0 1]      [2]           
                               = cons(mark(X1),X2)        
        
                 mark(from(X)) = [1 2] X + [3]            
                                 [0 1]     [3]            
                               > [1 2] X + [1]            
                                 [0 1]     [3]            
                               = a__from(mark(X))         
        
              mark(fst(X1,X2)) = [1 2] X1 + [1 2] X2 + [2]
                                 [0 1]      [0 1]      [2]
                               > [1 2] X1 + [1 2] X2 + [1]
                                 [0 1]      [0 1]      [2]
                               = a__fst(mark(X1),mark(X2))
        
                  mark(len(X)) = [1 4] X + [5]            
                                 [0 1]     [3]            
                               > [1 4] X + [3]            
                                 [0 1]     [3]            
                               = a__len(mark(X))          
        
                   mark(nil()) = [4]                      
                                 [4]                      
                               > [0]                      
                                 [4]                      
                               = nil()                    
        
                    mark(s(X)) = [8]                      
                                 [4]                      
                               > [4]                      
                                 [4]                      
                               = s(X)                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^2))