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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,h(y,z)) -> h(g(x,y),z)
            g(f(x,y),z) -> f(x,g(y,z))
            g(h(x,y),z) -> g(x,f(y,z))
        - Signature:
            {g/2} / {f/2,h/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g} and constructors {f,h}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          f :: ["A"(0) x "A"(14)] -(14)-> "A"(14)
          f :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          f :: ["A"(0) x "A"(9)] -(9)-> "A"(9)
          g :: ["A"(14) x "A"(9)] -(3)-> "A"(1)
          h :: ["A"(9) x "A"(9)] -(9)-> "A"(9)
          h :: ["A"(14) x "A"(14)] -(14)-> "A"(14)
          h :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "f_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "h_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1)
        

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