/export/starexec/sandbox2/solver/bin/starexec_run_tct_dc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))
* Step 1: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
        - Signature:
            {f/2} / {a/0}
        - Obligation:
             derivational complexity wrt. signature {a,f}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind triangular matrix interpretation:
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = [0]                      
                 [0]                      
          p(f) = [1 0] x1 + [1 1] x2 + [0]
                 [0 1]      [0 1]      [2]
        
        Following rules are strictly oriented:
        f(a(),f(f(a(),x),a())) = [1 2] x + [4]         
                                 [0 1]     [6]         
                               > [1 2] x + [2]         
                                 [0 1]     [6]         
                               = f(f(a(),f(a(),x)),a())
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
        - Signature:
            {f/2} / {a/0}
        - Obligation:
             derivational complexity wrt. signature {a,f}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))