WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0(),y,0(),u) -> true()
            f(0(),y,s(z),u) -> false()
            f(s(x),0(),z,u) -> f(x,u,minus(z,s(x)),u)
            f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
            perfectp(0()) -> false()
            perfectp(s(x)) -> f(x,s(0()),s(x),s(x))
        - Signature:
            {f/4,perfectp/1} / {0/0,false/0,if/3,le/2,minus/2,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,perfectp} and constructors {0,false,if,le,minus,s,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(if) = {3}
        
        Following symbols are considered usable:
          {f,perfectp}
        TcT has computed the following interpretation:
                 p(0) = [0]          
                 p(f) = [10] x1 + [1]
             p(false) = [0]          
                p(if) = [1] x3 + [2] 
                p(le) = [1] x2 + [0] 
             p(minus) = [0]          
          p(perfectp) = [10] x1 + [1]
                 p(s) = [1] x1 + [3] 
              p(true) = [0]          
        
        Following rules are strictly oriented:
          f(0(),y,0(),u) = [1]                                          
                         > [0]                                          
                         = true()                                       
        
         f(0(),y,s(z),u) = [1]                                          
                         > [0]                                          
                         = false()                                      
        
         f(s(x),0(),z,u) = [10] x + [31]                                
                         > [10] x + [1]                                 
                         = f(x,u,minus(z,s(x)),u)                       
        
        f(s(x),s(y),z,u) = [10] x + [31]                                
                         > [10] x + [3]                                 
                         = if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
        
           perfectp(0()) = [1]                                          
                         > [0]                                          
                         = false()                                      
        
          perfectp(s(x)) = [10] x + [31]                                
                         > [10] x + [1]                                 
                         = f(x,s(0()),s(x),s(x))                        
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))