/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> add0(Cons(Cons(Nil(),Nil()),x'),xs)
            goal(x,y) -> add0(x,y)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {add0/2,goal/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,notEmpty} and constructors {Cons,False,Nil
            ,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> add0(Cons(Cons(Nil(),Nil()),x'),xs)
            goal(x,y) -> add0(x,y)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {add0/2,goal/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,notEmpty} and constructors {Cons,False,Nil
            ,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          add0(x,z){z -> Cons(y,z)} =
            add0(x,Cons(y,z)) ->^+ add0(Cons(Cons(Nil(),Nil()),x),z)
              = C[add0(Cons(Cons(Nil(),Nil()),x),z) = add0(x,z){x -> Cons(Cons(Nil(),Nil()),x)}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            add0(x,Nil()) -> x
            add0(x',Cons(x,xs)) -> add0(Cons(Cons(Nil(),Nil()),x'),xs)
            goal(x,y) -> add0(x,y)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {add0/2,goal/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,notEmpty} and constructors {Cons,False,Nil
            ,True}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(0) x "A"(14)] -(14)-> "A"(14)
          Cons :: ["A"(0) x "A"(11)] -(11)-> "A"(11)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          False :: [] -(0)-> "A"(14)
          Nil :: [] -(0)-> "A"(14)
          Nil :: [] -(0)-> "A"(11)
          Nil :: [] -(0)-> "A"(0)
          True :: [] -(0)-> "A"(10)
          add0 :: ["A"(0) x "A"(14)] -(8)-> "A"(0)
          goal :: ["A"(4) x "A"(14)] -(13)-> "A"(0)
          notEmpty :: ["A"(11)] -(15)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "False_A" :: [] -(0)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "True_A" :: [] -(0)-> "A"(1)
        

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