WORST_CASE(?,O(n^1))
* Step 1: NaturalPI 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:
        NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        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) = 4          
              p(a__eq) = 3 + 2*x2   
             p(a__inf) = 7 + x1     
          p(a__length) = 4 + x1     
            p(a__take) = 3 + x1 + x2
               p(cons) = 1 + x2     
                 p(eq) = 2 + x2     
              p(false) = 1          
                p(inf) = 4 + x1     
             p(length) = 3 + x1     
               p(mark) = 2*x1       
                p(nil) = 4          
                  p(s) = 1 + x1     
               p(take) = 2 + x1 + x2
               p(true) = 4          
        
        Following rules are strictly oriented:
                     a__eq(X,Y) = 3 + 2*Y                   
                                > 1                         
                                = false()                   
        
                   a__eq(X1,X2) = 3 + 2*X2                  
                                > 2 + X2                    
                                = eq(X1,X2)                 
        
                 a__eq(0(),0()) = 11                        
                                > 4                         
                                = true()                    
        
               a__eq(s(X),s(Y)) = 5 + 2*Y                   
                                > 3 + 2*Y                   
                                = a__eq(X,Y)                
        
                      a__inf(X) = 7 + X                     
                                > 6 + X                     
                                = cons(X,inf(s(X)))         
        
                      a__inf(X) = 7 + X                     
                                > 4 + X                     
                                = inf(X)                    
        
                   a__length(X) = 4 + X                     
                                > 3 + X                     
                                = length(X)                 
        
           a__length(cons(X,L)) = 5 + L                     
                                > 4 + L                     
                                = s(length(L))              
        
               a__length(nil()) = 8                         
                                > 4                         
                                = 0()                       
        
                 a__take(X1,X2) = 3 + X1 + X2               
                                > 2 + X1 + X2               
                                = take(X1,X2)               
        
                 a__take(0(),X) = 7 + X                     
                                > 4                         
                                = nil()                     
        
        a__take(s(X),cons(Y,L)) = 5 + L + X                 
                                > 3 + L + X                 
                                = cons(Y,take(X,L))         
        
                      mark(0()) = 8                         
                                > 4                         
                                = 0()                       
        
              mark(cons(X1,X2)) = 2 + 2*X2                  
                                > 1 + X2                    
                                = cons(X1,X2)               
        
                mark(eq(X1,X2)) = 4 + 2*X2                  
                                > 3 + 2*X2                  
                                = a__eq(X1,X2)              
        
                  mark(false()) = 2                         
                                > 1                         
                                = false()                   
        
                   mark(inf(X)) = 8 + 2*X                   
                                > 7 + 2*X                   
                                = a__inf(mark(X))           
        
                mark(length(X)) = 6 + 2*X                   
                                > 4 + 2*X                   
                                = a__length(mark(X))        
        
                    mark(nil()) = 8                         
                                > 4                         
                                = nil()                     
        
                     mark(s(X)) = 2 + 2*X                   
                                > 1 + X                     
                                = s(X)                      
        
              mark(take(X1,X2)) = 4 + 2*X1 + 2*X2           
                                > 3 + 2*X1 + 2*X2           
                                = a__take(mark(X1),mark(X2))
        
                   mark(true()) = 8                         
                                > 4                         
                                = true()                    
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))