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


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WORST_CASE(?,O(n^1))
* Step 1: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))
        - Signature:
            {f/1} / {a/0,g/2,h/2}
        - Obligation:
             derivational complexity wrt. signature {a,f,g,h}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind triangular matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(a) = [0]                      
                 [1]                      
          p(f) = [1 4] x1 + [0]           
                 [0 0]      [0]           
          p(g) = [1 0] x1 + [1 1] x2 + [0]
                 [0 0]      [0 0]      [0]
          p(h) = [1 6] x1 + [1 0] x2 + [1]
                 [0 0]      [0 0]      [0]
        
        Following rules are strictly oriented:
        f(g(f(a()),h(a(),f(a())))) = [15]                                
                                     [0]                                 
                                   > [14]                                
                                     [0]                                 
                                   = f(h(g(f(a()),a()),g(f(a()),f(a()))))
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))
        - Signature:
            {f/1} / {a/0,g/2,h/2}
        - Obligation:
             derivational complexity wrt. signature {a,f,g,h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))