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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs)))
            duplicate(Nil()) -> Nil()
            goal(x) -> duplicate(x)
        - Signature:
            {duplicate/1,goal/1} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(11) x "A"(11)] -(11)-> "A"(11)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          Nil :: [] -(0)-> "A"(11)
          Nil :: [] -(0)-> "A"(6)
          duplicate :: ["A"(11)] -(1)-> "A"(0)
          goal :: ["A"(11)] -(16)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "Nil_A" :: [] -(0)-> "A"(1)
        

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