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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(c(X,s(Y))) -> f(c(s(X),Y))
            g(c(s(X),Y)) -> f(c(X,s(Y)))
        - Signature:
            {f/1,g/1} / {c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          c :: ["A"(0) x "A"(3)] -(3)-> "A"(3)
          c :: ["A"(0) x "A"(7)] -(7)-> "A"(7)
          f :: ["A"(3)] -(2)-> "A"(14)
          g :: ["A"(7)] -(7)-> "A"(6)
          s :: ["A"(3)] -(3)-> "A"(3)
          s :: ["A"(0)] -(0)-> "A"(0)
          s :: ["A"(4)] -(4)-> "A"(4)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "c_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "s_A" :: ["A"(1)] -(1)-> "A"(1)
        

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