/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:
            div2(0()) -> 0()
            div2(S(0())) -> 0()
            div2(S(S(x))) -> +(S(0()),div2(x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
        - Signature:
            {+/2,div2/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,div2} 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:
            div2(0()) -> 0()
            div2(S(0())) -> 0()
            div2(S(S(x))) -> +(S(0()),div2(x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
        - Signature:
            {+/2,div2/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,div2} and constructors {0,S}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          div2(x){x -> S(S(x))} =
            div2(S(S(x))) ->^+ +(S(0()),div2(x))
              = C[div2(x) = div2(x){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            div2(0()) -> 0()
            div2(S(0())) -> 0()
            div2(S(S(x))) -> +(S(0()),div2(x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
        - Signature:
            {+/2,div2/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,div2} and constructors {0,S}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          + :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          0 :: [] -(0)-> "A"(1)
          0 :: [] -(0)-> "A"(0)
          S :: ["A"(1)] -(1)-> "A"(1)
          S :: ["A"(0)] -(0)-> "A"(0)
          div2 :: ["A"(1)] -(2)-> "A"(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^1))