/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^2))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^2))
    + Considered Problem:
        - Strict TRS:
            f(0()) -> true()
            f(1()) -> false()
            f(s(x)) -> f(x)
            g(x,c(y)) -> g(x,g(s(c(y)),y))
            g(s(x),s(y)) -> if(f(x),s(x),s(y))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
        - Signature:
            {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(0()) -> true()
            f(1()) -> false()
            f(s(x)) -> f(x)
            g(x,c(y)) -> g(x,g(s(c(y)),y))
            g(s(x),s(y)) -> if(f(x),s(x),s(y))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
        - Signature:
            {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x){x -> s(x)} =
            f(s(x)) ->^+ f(x)
              = C[f(x) = f(x){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            f(0()) -> true()
            f(1()) -> false()
            f(s(x)) -> f(x)
            g(x,c(y)) -> g(x,g(s(c(y)),y))
            g(s(x),s(y)) -> if(f(x),s(x),s(y))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
        - Signature:
            {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(3, 0)
          1 :: [] -(0)-> "A"(3, 0)
          c :: ["A"(12, 8)] -(8)-> "A"(4, 8)
          c :: ["A"(7, 0)] -(0)-> "A"(7, 0)
          f :: ["A"(3, 0)] -(1)-> "A"(3, 2)
          false :: [] -(0)-> "A"(3, 0)
          false :: [] -(0)-> "A"(5, 4)
          g :: ["A"(7, 1) x "A"(4, 8)] -(0)-> "A"(4, 8)
          if :: ["A"(3, 0) x "A"(4, 8) x "A"(4, 10)] -(1)-> "A"(4, 8)
          s :: ["A"(3, 0)] -(3)-> "A"(3, 0)
          s :: ["A"(7, 0)] -(7)-> "A"(7, 1)
          s :: ["A"(4, 0)] -(4)-> "A"(4, 8)
          s :: ["A"(7, 0)] -(7)-> "A"(7, 9)
          s :: ["A"(4, 0)] -(4)-> "A"(4, 10)
          true :: [] -(0)-> "A"(3, 0)
          true :: [] -(0)-> "A"(4, 4)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(1, 0)
          "0_A" :: [] -(0)-> "A"(0, 1)
          "1_A" :: [] -(0)-> "A"(1, 0)
          "1_A" :: [] -(0)-> "A"(0, 1)
          "c_A" :: ["A"(1, 0)] -(0)-> "A"(1, 0)
          "c_A" :: ["A"(1, 1)] -(1)-> "A"(0, 1)
          "false_A" :: [] -(0)-> "A"(1, 0)
          "false_A" :: [] -(0)-> "A"(0, 1)
          "s_A" :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          "s_A" :: ["A"(0, 0)] -(0)-> "A"(0, 1)
          "true_A" :: [] -(0)-> "A"(1, 0)
          "true_A" :: [] -(0)-> "A"(0, 1)
        

WORST_CASE(Omega(n^1),O(n^2))