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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(f(a())) -> a__f(g(f(a())))
            mark(a()) -> a()
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
        - Signature:
            {a__f/1,mark/1} / {a/0,f/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,f,g}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          a :: [] -(0)-> "A"(4)
          a :: [] -(0)-> "A"(14)
          a :: [] -(0)-> "A"(10)
          a__f :: ["A"(4)] -(5)-> "A"(4)
          f :: ["A"(4)] -(4)-> "A"(4)
          f :: ["A"(14)] -(14)-> "A"(14)
          f :: ["A"(0)] -(0)-> "A"(0)
          g :: ["A"(0)] -(0)-> "A"(14)
          mark :: ["A"(14)] -(8)-> "A"(4)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "a_A" :: [] -(0)-> "A"(1)
          "f_A" :: ["A"(1)] -(1)-> "A"(1)
          "g_A" :: ["A"(0)] -(0)-> "A"(1)
        

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