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

** Step 1.b:1: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            double(0()) -> 0()
            double(s(x)) -> s(s(double(x)))
            sqr(0()) -> 0()
            sqr(s(x)) -> +(sqr(x),s(double(x)))
            sqr(s(x)) -> s(+(sqr(x),double(x)))
        - Signature:
            {+/2,double/1,sqr/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,double,sqr} and constructors {0,s}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          + :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(0, 0)
          0 :: [] -(0)-> "A"(1, 0)
          0 :: [] -(0)-> "A"(3, 0)
          0 :: [] -(0)-> "A"(4, 3)
          0 :: [] -(0)-> "A"(0, 0)
          double :: ["A"(3, 0)] -(1)-> "A"(1, 0)
          s :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          s :: ["A"(3, 0)] -(3)-> "A"(3, 0)
          s :: ["A"(7, 3)] -(4)-> "A"(4, 3)
          s :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          sqr :: ["A"(4, 3)] -(1)-> "A"(0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(0)
          "s_A" :: ["A"(0)] -(0)-> "A"(0)
        

WORST_CASE(Omega(n^1),O(n^2))