/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^2))
* Step 1: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            .(.(x,y),z) -> .(x,.(y,z))
        - Signature:
            {./2} / {}
        - Obligation:
             derivational complexity wrt. signature {.}
    + 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(.) = [1 1] x1 + [1 0] x2 + [0]
                 [0 1]      [0 1]      [8]
        
        Following rules are strictly oriented:
        .(.(x,y),z) = [1 2] x + [1 1] y + [1 0] z + [8] 
                      [0 1]     [0 1]     [0 1]     [16]
                    > [1 1] x + [1 1] y + [1 0] z + [0] 
                      [0 1]     [0 1]     [0 1]     [16]
                    = .(x,.(y,z))                       
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            .(.(x,y),z) -> .(x,.(y,z))
        - Signature:
            {./2} / {}
        - Obligation:
             derivational complexity wrt. signature {.}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))