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()) -> c6()
            CONV(s(z0)) -> c7(CONV(half(s(z0))),HALF(s(z0)))
            CONV(s(z0)) -> c8(LASTBIT(s(z0)))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            LASTBIT(0()) -> c3()
            LASTBIT(s(0())) -> c4()
            LASTBIT(s(s(z0))) -> c5(LASTBIT(z0))
        - Weak TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(z0)) -> cons(conv(half(s(z0))),lastbit(s(z0)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(z0))) -> lastbit(z0)
        - Signature:
            {CONV/1,HALF/1,LASTBIT/1,conv/1,half/1,lastbit/1} / {0/0,c/0,c1/0,c2/1,c3/0,c4/0,c5/1,c6/0,c7/2,c8/1,cons/2
            ,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {CONV,HALF,LASTBIT,conv,half,lastbit} and constructors {0
            ,c,c1,c2,c3,c4,c5,c6,c7,c8,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            CONV(0()) -> c6()
            CONV(s(z0)) -> c7(CONV(half(s(z0))),HALF(s(z0)))
            CONV(s(z0)) -> c8(LASTBIT(s(z0)))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            LASTBIT(0()) -> c3()
            LASTBIT(s(0())) -> c4()
            LASTBIT(s(s(z0))) -> c5(LASTBIT(z0))
        - Weak TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(z0)) -> cons(conv(half(s(z0))),lastbit(s(z0)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(z0))) -> lastbit(z0)
        - Signature:
            {CONV/1,HALF/1,LASTBIT/1,conv/1,half/1,lastbit/1} / {0/0,c/0,c1/0,c2/1,c3/0,c4/0,c5/1,c6/0,c7/2,c8/1,cons/2
            ,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {CONV,HALF,LASTBIT,conv,half,lastbit} and constructors {0
            ,c,c1,c2,c3,c4,c5,c6,c7,c8,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            CONV(0()) -> c6()
            CONV(s(z0)) -> c7(CONV(half(s(z0))),HALF(s(z0)))
            CONV(s(z0)) -> c8(LASTBIT(s(z0)))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            LASTBIT(0()) -> c3()
            LASTBIT(s(0())) -> c4()
            LASTBIT(s(s(z0))) -> c5(LASTBIT(z0))
        - Weak TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(z0)) -> cons(conv(half(s(z0))),lastbit(s(z0)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(z0))) -> lastbit(z0)
        - Signature:
            {CONV/1,HALF/1,LASTBIT/1,conv/1,half/1,lastbit/1} / {0/0,c/0,c1/0,c2/1,c3/0,c4/0,c5/1,c6/0,c7/2,c8/1,cons/2
            ,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {CONV,HALF,LASTBIT,conv,half,lastbit} and constructors {0
            ,c,c1,c2,c3,c4,c5,c6,c7,c8,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))) ->^+ c2(HALF(x))
              = C[HALF(x) = HALF(x){}]

** Step 1.b:1: Ara.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            CONV(0()) -> c6()
            CONV(s(z0)) -> c7(CONV(half(s(z0))),HALF(s(z0)))
            CONV(s(z0)) -> c8(LASTBIT(s(z0)))
            HALF(0()) -> c()
            HALF(s(0())) -> c1()
            HALF(s(s(z0))) -> c2(HALF(z0))
            LASTBIT(0()) -> c3()
            LASTBIT(s(0())) -> c4()
            LASTBIT(s(s(z0))) -> c5(LASTBIT(z0))
        - Weak TRS:
            conv(0()) -> cons(nil(),0())
            conv(s(z0)) -> cons(conv(half(s(z0))),lastbit(s(z0)))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(z0))) -> s(half(z0))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(z0))) -> lastbit(z0)
        - Signature:
            {CONV/1,HALF/1,LASTBIT/1,conv/1,half/1,lastbit/1} / {0/0,c/0,c1/0,c2/1,c3/0,c4/0,c5/1,c6/0,c7/2,c8/1,cons/2
            ,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {CONV,HALF,LASTBIT,conv,half,lastbit} and constructors {0
            ,c,c1,c2,c3,c4,c5,c6,c7,c8,cons,nil,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(6)
          F (TrsFun "0") :: [] -(0)-> "A"(1)
          F (TrsFun "0") :: [] -(0)-> "A"(3)
          F (TrsFun "0") :: [] -(0)-> "A"(0)
          F (TrsFun "CONV") :: ["A"(6)] -(1)-> "A"(0)
          F (TrsFun "HALF") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "LASTBIT") :: ["A"(3)] -(1)-> "A"(0)
          F (TrsFun "c") :: [] -(0)-> "A"(0)
          F (TrsFun "c1") :: [] -(0)-> "A"(0)
          F (TrsFun "c2") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c3") :: [] -(0)-> "A"(0)
          F (TrsFun "c4") :: [] -(0)-> "A"(0)
          F (TrsFun "c5") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "c6") :: [] -(0)-> "A"(0)
          F (TrsFun "c7") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "c8") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "cons") :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          F (TrsFun "conv") :: ["A"(3)] -(0)-> "A"(0)
          F (TrsFun "half") :: ["A"(3)] -(0)-> "A"(6)
          F (TrsFun "lastbit") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "nil") :: [] -(0)-> "A"(0)
          F (TrsFun "s") :: ["A"(6)] -(6)-> "A"(6)
          F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1)
          F (TrsFun "s") :: ["A"(3)] -(3)-> "A"(3)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        

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