/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(f(x)) -> g(f(x))
            g(g(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {}
        - Obligation:
             derivational complexity wrt. signature {f,g}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, 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(f) = [1] x1 + [48]
          p(g) = [1] x1 + [47]
        
        Following rules are strictly oriented:
        f(f(x)) = [1] x + [96]
                > [1] x + [95]
                = g(f(x))     
        
        g(g(x)) = [1] x + [94]
                > [1] x + [48]
                = f(x)        
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(f(x)) -> g(f(x))
            g(g(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {}
        - Obligation:
             derivational complexity wrt. signature {f,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))