/export/starexec/sandbox2/solver/bin/starexec_run_tct_dci /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:
            0(x1) -> 1(x1)
            4(5(4(5(x1)))) -> 4(4(5(5(x1))))
            5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)
        - Signature:
            {0/1,4/1,5/1} / {1/1,2/1}
        - Obligation:
            innermost derivational complexity wrt. signature {0,1,2,4,5}
    + 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(0) = [1] x1 + [9]
          p(1) = [1] x1 + [7]
          p(2) = [1] x1 + [0]
          p(4) = [1] x1 + [3]
          p(5) = [1] x1 + [0]
        
        Following rules are strictly oriented:
                                         0(x1) = [1] x1 + [9] 
                                               > [1] x1 + [7] 
                                               = 1(x1)        
        
        5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) = [1] x1 + [18]
                                               > [1] x1 + [0] 
                                               = 2(x1)        
        
        
        Following rules are (at-least) weakly oriented:
        4(5(4(5(x1)))) =  [1] x1 + [6]  
                       >= [1] x1 + [6]  
                       =  4(4(5(5(x1))))
        
* Step 2: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            4(5(4(5(x1)))) -> 4(4(5(5(x1))))
        - Weak TRS:
            0(x1) -> 1(x1)
            5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)
        - Signature:
            {0/1,4/1,5/1} / {1/1,2/1}
        - Obligation:
            innermost derivational complexity wrt. signature {0,1,2,4,5}
    + 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(0) = [1 0] x1 + [0]
                 [0 0]      [0]
          p(1) = [1 0] x1 + [0]
                 [0 0]      [0]
          p(2) = [1 0] x1 + [1]
                 [0 0]      [0]
          p(4) = [1 0] x1 + [0]
                 [0 0]      [1]
          p(5) = [1 1] x1 + [0]
                 [0 0]      [0]
        
        Following rules are strictly oriented:
        4(5(4(5(x1)))) = [1 1] x1 + [1]
                         [0 0]      [1]
                       > [1 1] x1 + [0]
                         [0 0]      [1]
                       = 4(4(5(5(x1))))
        
        
        Following rules are (at-least) weakly oriented:
                                         0(x1) =  [1 0] x1 + [0]
                                                  [0 0]      [0]
                                               >= [1 0] x1 + [0]
                                                  [0 0]      [0]
                                               =  1(x1)         
        
        5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) =  [1 0] x1 + [1]
                                                  [0 0]      [0]
                                               >= [1 0] x1 + [1]
                                                  [0 0]      [0]
                                               =  2(x1)         
        
* Step 3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            0(x1) -> 1(x1)
            4(5(4(5(x1)))) -> 4(4(5(5(x1))))
            5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)
        - Signature:
            {0/1,4/1,5/1} / {1/1,2/1}
        - Obligation:
            innermost derivational complexity wrt. signature {0,1,2,4,5}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))