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

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

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