/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,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:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          anchored(y,z){y -> Cons(x,y)} =
            anchored(Cons(x,y),z) ->^+ anchored(y,Cons(Cons(Nil(),Nil()),z))
              = C[anchored(y,Cons(Cons(Nil(),Nil()),z)) = anchored(y,z){z -> Cons(Cons(Nil(),Nil()),z)}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            anchored(Cons(x,xs),y) -> anchored(xs,Cons(Cons(Nil(),Nil()),y))
            anchored(Nil(),y) -> y
            goal(x,y) -> anchored(x,y)
        - Signature:
            {anchored/2,goal/2} / {Cons/2,Nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {anchored,goal} and constructors {Cons,Nil}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          Cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          Cons :: ["A"(4) x "A"(4)] -(4)-> "A"(4)
          Nil :: [] -(0)-> "A"(15)
          Nil :: [] -(0)-> "A"(14)
          anchored :: ["A"(15) x "A"(0)] -(10)-> "A"(0)
          goal :: ["A"(15) x "A"(6)] -(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))