WORST_CASE(?,O(n^1))
* Step 1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            filter(cons(X),0(),M) -> cons(0())
            filter(cons(X),s(N),M) -> cons(X)
            nats(N) -> cons(N)
            sieve(cons(0())) -> cons(0())
            sieve(cons(s(N))) -> cons(s(N))
            zprimes() -> sieve(nats(s(s(0()))))
        - Signature:
            {filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {filter,nats,sieve,zprimes} and constructors {0,cons,s}
    + Applied Processor:
        NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(stronglyLinear):
        The following argument positions are considered usable:
          uargs(sieve) = {1}
        
        Following symbols are considered usable:
          {filter,nats,sieve,zprimes}
        TcT has computed the following interpretation:
                p(0) = 1               
             p(cons) = x1              
           p(filter) = 6 + x1 + x2 + x3
             p(nats) = 1 + x1          
                p(s) = 2 + x1          
            p(sieve) = 6 + x1          
          p(zprimes) = 14              
        
        Following rules are strictly oriented:
         filter(cons(X),0(),M) = 7 + M + X             
                               > 1                     
                               = cons(0())             
        
        filter(cons(X),s(N),M) = 8 + M + N + X         
                               > X                     
                               = cons(X)               
        
                       nats(N) = 1 + N                 
                               > N                     
                               = cons(N)               
        
              sieve(cons(0())) = 7                     
                               > 1                     
                               = cons(0())             
        
             sieve(cons(s(N))) = 8 + N                 
                               > 2 + N                 
                               = cons(s(N))            
        
                     zprimes() = 14                    
                               > 12                    
                               = sieve(nats(s(s(0()))))
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))