/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(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(xs,ys) -> merge(xs,ys)
            merge(Cons(x,xs),Nil()) -> Cons(x,xs)
            merge(Cons(x',xs'),Cons(x,xs)) -> merge[Ite](<=(x',x),Cons(x',xs'),Cons(x,xs))
            merge(Nil(),ys) -> ys
        - Weak TRS:
            <=(0(),y) -> True()
            <=(S(x),0()) -> False()
            <=(S(x),S(y)) -> <=(x,y)
            merge[Ite](False(),xs',Cons(x,xs)) -> Cons(x,merge(xs',xs))
            merge[Ite](True(),Cons(x,xs),ys) -> Cons(x,merge(xs,ys))
        - Signature:
            {<=/2,goal/2,merge/2,merge[Ite]/3} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<=,goal,merge,merge[Ite]} and constructors {0,Cons,False
            ,Nil,S,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(xs,ys) -> merge(xs,ys)
            merge(Cons(x,xs),Nil()) -> Cons(x,xs)
            merge(Cons(x',xs'),Cons(x,xs)) -> merge[Ite](<=(x',x),Cons(x',xs'),Cons(x,xs))
            merge(Nil(),ys) -> ys
        - Weak TRS:
            <=(0(),y) -> True()
            <=(S(x),0()) -> False()
            <=(S(x),S(y)) -> <=(x,y)
            merge[Ite](False(),xs',Cons(x,xs)) -> Cons(x,merge(xs',xs))
            merge[Ite](True(),Cons(x,xs),ys) -> Cons(x,merge(xs,ys))
        - Signature:
            {<=/2,goal/2,merge/2,merge[Ite]/3} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<=,goal,merge,merge[Ite]} and constructors {0,Cons,False
            ,Nil,S,True}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(0)
          <= :: ["A"(0) x "A"(0)] -(0)-> "A"(6)
          Cons :: ["A"(0) x "A"(11)] -(11)-> "A"(11)
          Cons :: ["A"(0) x "A"(15)] -(15)-> "A"(15)
          Cons :: ["A"(0) x "A"(2)] -(2)-> "A"(2)
          Cons :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          False :: [] -(0)-> "A"(3)
          False :: [] -(0)-> "A"(6)
          Nil :: [] -(0)-> "A"(15)
          Nil :: [] -(0)-> "A"(11)
          S :: ["A"(0)] -(0)-> "A"(0)
          True :: [] -(0)-> "A"(3)
          True :: [] -(0)-> "A"(6)
          goal :: ["A"(11) x "A"(15)] -(15)-> "A"(0)
          merge :: ["A"(11) x "A"(15)] -(12)-> "A"(1)
          merge[Ite] :: ["A"(3) x "A"(11) x "A"(15)] -(7)-> "A"(1)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(1)
          "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "False_A" :: [] -(0)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
          "S_A" :: ["A"(1)] -(1)-> "A"(1)
          "True_A" :: [] -(0)-> "A"(1)
        

WORST_CASE(?,O(n^1))