/export/starexec/sandbox/solver/bin/starexec_run_tct_dci /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,z),y)
            -(+(x,y),y) -> x
        - Signature:
            {+/2,-/2} / {}
        - Obligation:
            innermost derivational complexity wrt. signature {+,-}
    + 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(+) = [1] x1 + [1] x2 + [3]
          p(-) = [1] x1 + [1] x2 + [4]
        
        Following rules are strictly oriented:
        -(+(x,y),y) = [1] x + [2] y + [7]
                    > [1] x + [0]        
                    = x                  
        
        
        Following rules are (at-least) weakly oriented:
        +(-(x,y),z) =  [1] x + [1] y + [1] z + [7]
                    >= [1] x + [1] y + [1] z + [7]
                    =  -(+(x,z),y)                
        
* Step 2: NaturalMI.  WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            +(-(x,y),z) -> -(+(x,z),y)
        - Weak TRS:
            -(+(x,y),y) -> x
        - Signature:
            {+/2,-/2} / {}
        - Obligation:
            innermost 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 2] x1 + [1 3] x2 + [0]
                 [0 1]      [0 0]      [3]
          p(-) = [1 3] x1 + [1 2] x2 + [1]
                 [0 1]      [0 1]      [5]
        
        Following rules are strictly oriented:
        +(-(x,y),z) = [1 5] x + [1 4] y + [1 3] z + [11]
                      [0 1]     [0 1]     [0 0]     [8] 
                    > [1 5] x + [1 2] y + [1 3] z + [10]
                      [0 1]     [0 1]     [0 0]     [8] 
                    = -(+(x,z),y)                       
        
        
        Following rules are (at-least) weakly oriented:
        -(+(x,y),y) =  [1 5] x + [2 5] y + [10]
                       [0 1]     [0 1]     [8] 
                    >= [1 0] x + [0]           
                       [0 1]     [0]           
                    =  x                       
        
* Step 3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(-(x,y),z) -> -(+(x,z),y)
            -(+(x,y),y) -> x
        - Signature:
            {+/2,-/2} / {}
        - Obligation:
            innermost derivational complexity wrt. signature {+,-}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))