WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__eq(X,Y) -> false()
            a__eq(X1,X2) -> eq(X1,X2)
            a__eq(0(),0()) -> true()
            a__eq(s(X),s(Y)) -> a__eq(X,Y)
            a__inf(X) -> cons(X,inf(s(X)))
            a__inf(X) -> inf(X)
            a__length(X) -> length(X)
            a__length(cons(X,L)) -> s(length(L))
            a__length(nil()) -> 0()
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),X) -> nil()
            a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(eq(X1,X2)) -> a__eq(X1,X2)
            mark(false()) -> false()
            mark(inf(X)) -> a__inf(mark(X))
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
            mark(true()) -> true()
        - Signature:
            {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
            ,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0
            ,cons,eq,false,inf,length,nil,s,take,true}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, 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__inf) = {1},
          uargs(a__length) = {1},
          uargs(a__take) = {1,2}
        
        Following symbols are considered usable:
          {a__eq,a__inf,a__length,a__take,mark}
        TcT has computed the following interpretation:
                  p(0) = [1]                  
              p(a__eq) = [4] x2 + [4]         
             p(a__inf) = [1] x1 + [10]        
          p(a__length) = [1] x1 + [7]         
            p(a__take) = [1] x1 + [1] x2 + [8]
               p(cons) = [1] x2 + [0]         
                 p(eq) = [1] x2 + [2]         
              p(false) = [0]                  
                p(inf) = [1] x1 + [4]         
             p(length) = [1] x1 + [2]         
               p(mark) = [4] x1 + [1]         
                p(nil) = [4]                  
                  p(s) = [1] x1 + [4]         
               p(take) = [1] x1 + [1] x2 + [3]
               p(true) = [0]                  
        
        Following rules are strictly oriented:
                     a__eq(X,Y) = [4] Y + [4]               
                                > [0]                       
                                = false()                   
        
                   a__eq(X1,X2) = [4] X2 + [4]              
                                > [1] X2 + [2]              
                                = eq(X1,X2)                 
        
                 a__eq(0(),0()) = [8]                       
                                > [0]                       
                                = true()                    
        
               a__eq(s(X),s(Y)) = [4] Y + [20]              
                                > [4] Y + [4]               
                                = a__eq(X,Y)                
        
                      a__inf(X) = [1] X + [10]              
                                > [1] X + [8]               
                                = cons(X,inf(s(X)))         
        
                      a__inf(X) = [1] X + [10]              
                                > [1] X + [4]               
                                = inf(X)                    
        
                   a__length(X) = [1] X + [7]               
                                > [1] X + [2]               
                                = length(X)                 
        
           a__length(cons(X,L)) = [1] L + [7]               
                                > [1] L + [6]               
                                = s(length(L))              
        
               a__length(nil()) = [11]                      
                                > [1]                       
                                = 0()                       
        
                 a__take(X1,X2) = [1] X1 + [1] X2 + [8]     
                                > [1] X1 + [1] X2 + [3]     
                                = take(X1,X2)               
        
                 a__take(0(),X) = [1] X + [9]               
                                > [4]                       
                                = nil()                     
        
        a__take(s(X),cons(Y,L)) = [1] L + [1] X + [12]      
                                > [1] L + [1] X + [3]       
                                = cons(Y,take(X,L))         
        
                      mark(0()) = [5]                       
                                > [1]                       
                                = 0()                       
        
              mark(cons(X1,X2)) = [4] X2 + [1]              
                                > [1] X2 + [0]              
                                = cons(X1,X2)               
        
                mark(eq(X1,X2)) = [4] X2 + [9]              
                                > [4] X2 + [4]              
                                = a__eq(X1,X2)              
        
                  mark(false()) = [1]                       
                                > [0]                       
                                = false()                   
        
                   mark(inf(X)) = [4] X + [17]              
                                > [4] X + [11]              
                                = a__inf(mark(X))           
        
                mark(length(X)) = [4] X + [9]               
                                > [4] X + [8]               
                                = a__length(mark(X))        
        
                    mark(nil()) = [17]                      
                                > [4]                       
                                = nil()                     
        
                     mark(s(X)) = [4] X + [17]              
                                > [1] X + [4]               
                                = s(X)                      
        
              mark(take(X1,X2)) = [4] X1 + [4] X2 + [13]    
                                > [4] X1 + [4] X2 + [10]    
                                = a__take(mark(X1),mark(X2))
        
                   mark(true()) = [1]                       
                                > [0]                       
                                = true()                    
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))