/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:
            f(x1,0()) -> g(x1,0())
            f(y,S(x)) -> f(S(y),x)
            g(0(),x2) -> x2
            g(S(x),y) -> g(x,S(y))
        - Signature:
            {f/2,g/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} 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:
            f(x1,0()) -> g(x1,0())
            f(y,S(x)) -> f(S(y),x)
            g(0(),x2) -> x2
            g(S(x),y) -> g(x,S(y))
        - Signature:
            {f/2,g/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,S}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x,y){y -> S(y)} =
            f(x,S(y)) ->^+ f(S(x),y)
              = C[f(S(x),y) = f(x,y){x -> S(x)}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(x1,0()) -> g(x1,0())
            f(y,S(x)) -> f(S(y),x)
            g(0(),x2) -> x2
            g(S(x),y) -> g(x,S(y))
        - Signature:
            {f/2,g/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,S}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(15)
          0 :: [] -(0)-> "A"(13)
          0 :: [] -(0)-> "A"(14)
          S :: ["A"(15)] -(15)-> "A"(15)
          S :: ["A"(13)] -(13)-> "A"(13)
          S :: ["A"(12)] -(12)-> "A"(12)
          f :: ["A"(13) x "A"(15)] -(15)-> "A"(3)
          g :: ["A"(13) x "A"(12)] -(12)-> "A"(6)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(1)
          "S_A" :: ["A"(1)] -(1)-> "A"(1)
        

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