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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a,cons(x,k)) -> f(cons(x,a),k)
            f(a,empty()) -> g(a,empty())
            g(cons(x,k),d) -> g(k,cons(x,d))
            g(empty(),d) -> d
        - Signature:
            {f/2,g/2} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          cons :: ["A"(15) x "A"(15)] -(15)-> "A"(15)
          cons :: ["A"(7) x "A"(7)] -(7)-> "A"(7)
          cons :: ["A"(2) x "A"(2)] -(2)-> "A"(2)
          empty :: [] -(0)-> "A"(15)
          empty :: [] -(0)-> "A"(7)
          empty :: [] -(0)-> "A"(8)
          f :: ["A"(7) x "A"(15)] -(9)-> "A"(2)
          g :: ["A"(7) x "A"(2)] -(6)-> "A"(2)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
          "empty_A" :: [] -(0)-> "A"(1)
        

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