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

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(x,g(y,z)) -> g(f(x,y),z)
            f(x,nil()) -> g(nil(),x)
            norm(g(x,y)) -> s(norm(x))
            norm(nil()) -> 0()
            rem(g(x,y),0()) -> g(x,y)
            rem(g(x,y),s(z)) -> rem(x,z)
            rem(nil(),y) -> nil()
        - Signature:
            {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,norm,rem} and constructors {0,g,nil,s}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(9)
          0 :: [] -(0)-> "A"(14)
          f :: ["A"(12) x "A"(8)] -(8)-> "A"(0)
          g :: ["A"(8) x "A"(0)] -(8)-> "A"(8)
          g :: ["A"(15) x "A"(0)] -(15)-> "A"(15)
          g :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          nil :: [] -(0)-> "A"(8)
          nil :: [] -(0)-> "A"(15)
          nil :: [] -(0)-> "A"(0)
          nil :: [] -(0)-> "A"(14)
          norm :: ["A"(15)] -(1)-> "A"(4)
          rem :: ["A"(0) x "A"(9)] -(8)-> "A"(0)
          s :: ["A"(9)] -(9)-> "A"(9)
          s :: ["A"(4)] -(4)-> "A"(4)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(1)
          "g_A" :: ["A"(1) x "A"(0)] -(1)-> "A"(1)
          "nil_A" :: [] -(0)-> "A"(1)
          "s_A" :: ["A"(1)] -(1)-> "A"(1)
        

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