WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
        - Signature:
            {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
        - Signature:
            {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          half(x){x -> s(s(x))} =
            half(s(s(x))) ->^+ s(half(x))
              = C[half(x) = half(x){}]

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
        - Signature:
            {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(cons) = {1,2},
          uargs(conv) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {conv,half,lastbit}
        TcT has computed the following interpretation:
                p(0) = 0       
             p(cons) = x1 + x2 
             p(conv) = 2 + 4*x1
             p(half) = 0       
          p(lastbit) = 4*x1    
              p(nil) = 0       
                p(s) = x1      
        
        Following rules are strictly oriented:
        conv(0()) = 2              
                  > 0              
                  = cons(nil(),0())
        
        
        Following rules are (at-least) weakly oriented:
              conv(s(x)) =  2 + 4*x                             
                         >= 2 + 4*x                             
                         =  cons(conv(half(s(x))),lastbit(s(x)))
        
               half(0()) =  0                                   
                         >= 0                                   
                         =  0()                                 
        
            half(s(0())) =  0                                   
                         >= 0                                   
                         =  0()                                 
        
           half(s(s(x))) =  0                                   
                         >= 0                                   
                         =  s(half(x))                          
        
            lastbit(0()) =  0                                   
                         >= 0                                   
                         =  0()                                 
        
         lastbit(s(0())) =  0                                   
                         >= 0                                   
                         =  s(0())                              
        
        lastbit(s(s(x))) =  4*x                                 
                         >= 4*x                                 
                         =  lastbit(x)                          
        
** Step 1.b:2: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
        - Weak TRS:
            conv(0()) -> cons(nil(),0())
        - Signature:
            {conv/1,half/1,lastbit/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv,half,lastbit} and constructors {0,cons,nil,s}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 1, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(5)
          0 :: [] -(0)-> "A"(1)
          0 :: [] -(0)-> "A"(9)
          0 :: [] -(0)-> "A"(0)
          cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          conv :: ["A"(9)] -(0)-> "A"(0)
          half :: ["A"(5)] -(1)-> "A"(9)
          lastbit :: ["A"(1)] -(1)-> "A"(0)
          nil :: [] -(0)-> "A"(0)
          s :: ["A"(9)] -(9)-> "A"(9)
          s :: ["A"(5)] -(5)-> "A"(5)
          s :: ["A"(1)] -(1)-> "A"(1)
          s :: ["A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        

WORST_CASE(Omega(n^1),O(n^1))