/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:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            s(X) -> n__s(X)
        - Signature:
            {2nd/1,activate/1,from/1,s/1} / {cons/2,cons1/2,n__from/1,n__s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,from,s} and constructors {cons,cons1,n__from
            ,n__s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            s(X) -> n__s(X)
        - Signature:
            {2nd/1,activate/1,from/1,s/1} / {cons/2,cons1/2,n__from/1,n__s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,from,s} and constructors {cons,cons1,n__from
            ,n__s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__from(x)} =
            activate(n__from(x)) ->^+ from(activate(x))
              = C[activate(x) = activate(x){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(activate(X))
            activate(n__s(X)) -> s(activate(X))
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            s(X) -> n__s(X)
        - Signature:
            {2nd/1,activate/1,from/1,s/1} / {cons/2,cons1/2,n__from/1,n__s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,from,s} and constructors {cons,cons1,n__from
            ,n__s}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          2nd :: ["A"(15)] -(8)-> "A"(0)
          activate :: ["A"(15)] -(13)-> "A"(0)
          cons :: ["A"(0) x "A"(15)] -(15)-> "A"(15)
          cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          cons1 :: ["A"(0) x "A"(0)] -(0)-> "A"(15)
          from :: ["A"(0)] -(2)-> "A"(0)
          n__from :: ["A"(15)] -(15)-> "A"(15)
          n__from :: ["A"(0)] -(0)-> "A"(0)
          n__s :: ["A"(15)] -(15)-> "A"(15)
          n__s :: ["A"(0)] -(0)-> "A"(0)
          s :: ["A"(0)] -(7)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "cons1_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(1)
          "cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "n__from_A" :: ["A"(0)] -(1)-> "A"(1)
          "n__s_A" :: ["A"(0)] -(1)-> "A"(1)
        

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