/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__c(X) -> c(X)
            a__c(X) -> d(X)
            a__f(X) -> f(X)
            a__f(f(X)) -> a__c(f(g(f(X))))
            a__h(X) -> a__c(d(X))
            a__h(X) -> h(X)
            mark(c(X)) -> a__c(X)
            mark(d(X)) -> d(X)
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__c(X) -> c(X)
            a__c(X) -> d(X)
            a__f(X) -> f(X)
            a__f(f(X)) -> a__c(f(g(f(X))))
            a__h(X) -> a__c(d(X))
            a__h(X) -> h(X)
            mark(c(X)) -> a__c(X)
            mark(d(X)) -> d(X)
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h}
    + 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__c(X) -> c(X)
            a__c(X) -> d(X)
            a__f(X) -> f(X)
            a__f(f(X)) -> a__c(f(g(f(X))))
            a__h(X) -> a__c(d(X))
            a__h(X) -> h(X)
            mark(c(X)) -> a__c(X)
            mark(d(X)) -> d(X)
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(X)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__c,a__f,a__h,mark} and constructors {c,d,f,g,h}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          a__c :: ["A"(0)] -(1)-> "A"(0)
          a__f :: ["A"(0)] -(2)-> "A"(0)
          a__h :: ["A"(0)] -(2)-> "A"(0)
          c :: ["A"(3)] -(3)-> "A"(3)
          c :: ["A"(0)] -(0)-> "A"(0)
          d :: ["A"(3)] -(3)-> "A"(3)
          d :: ["A"(0)] -(0)-> "A"(0)
          f :: ["A"(0)] -(0)-> "A"(0)
          f :: ["A"(3)] -(3)-> "A"(3)
          g :: ["A"(3)] -(3)-> "A"(3)
          g :: ["A"(0)] -(0)-> "A"(0)
          h :: ["A"(3)] -(3)-> "A"(3)
          h :: ["A"(0)] -(0)-> "A"(0)
          mark :: ["A"(3)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "c_A" :: ["A"(0)] -(0)-> "A"(0)
          "d_A" :: ["A"(0)] -(0)-> "A"(0)
          "f_A" :: ["A"(0)] -(0)-> "A"(0)
          "g_A" :: ["A"(0)] -(0)-> "A"(0)
          "h_A" :: ["A"(0)] -(0)-> "A"(0)
        

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