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

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

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