/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^1))
* Step 1: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(a(x)) -> a(b(a(x)))
        - Signature:
            {a/1} / {b/1}
        - Obligation:
             derivational complexity wrt. signature {a,b}
    + 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) = [1 8] x1 + [0]
                 [0 0]      [2]
          p(b) = [1 2] x1 + [0]
                 [0 0]      [0]
        
        Following rules are strictly oriented:
        a(a(x)) = [1 8] x + [16]
                  [0 0]     [2] 
                > [1 8] x + [4] 
                  [0 0]     [2] 
                = a(b(a(x)))    
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(a(x)) -> a(b(a(x)))
        - Signature:
            {a/1} / {b/1}
        - Obligation:
             derivational complexity wrt. signature {a,b}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))