/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,*(y,z))
            +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
        - Signature:
            {*/2,+/2} / {a/0}
        - Obligation:
            innermost derivational complexity wrt. signature {*,+,a}
    + 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(*) = [1 0] x1 + [1 1] x2 + [4]
                 [0 0]      [0 0]      [0]
          p(+) = [1 0] x1 + [1 0] x2 + [1]
                 [0 0]      [0 0]      [2]
          p(a) = [3]                      
                 [0]                      
        
        Following rules are strictly oriented:
        +(*(x,y),*(a(),y)) = [1 0] x + [2 2] y + [12]
                             [0 0]     [0 0]     [2] 
                           > [1 0] x + [1 1] y + [8] 
                             [0 0]     [0 0]     [0] 
                           = *(+(x,a()),y)           
        
        
        Following rules are (at-least) weakly oriented:
        *(*(x,y),z) =  [1 0] x + [1 1] y + [1 1] z + [8]
                       [0 0]     [0 0]     [0 0]     [0]
                    >= [1 0] x + [1 0] y + [1 1] z + [8]
                       [0 0]     [0 0]     [0 0]     [0]
                    =  *(x,*(y,z))                      
        
* Step 2: NaturalMI.  WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(*(x,y),z) -> *(x,*(y,z))
        - Weak TRS:
            +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
        - Signature:
            {*/2,+/2} / {a/0}
        - Obligation:
            innermost derivational complexity wrt. signature {*,+,a}
    + 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 + [3]
                 [0 1]      [0 1]      [2]
          p(+) = [1 0] x1 + [1 2] x2 + [1]
                 [0 1]      [0 0]      [4]
          p(a) = [1]                      
                 [1]                      
        
        Following rules are strictly oriented:
        *(*(x,y),z) = [1 2] x + [1 1] y + [1 0] z + [8]
                      [0 1]     [0 1]     [0 1]     [4]
                    > [1 1] x + [1 1] y + [1 0] z + [6]
                      [0 1]     [0 1]     [0 1]     [4]
                    = *(x,*(y,z))                      
        
        
        Following rules are (at-least) weakly oriented:
        +(*(x,y),*(a(),y)) =  [1 1] x + [2 2] y + [15]
                              [0 1]     [0 1]     [6] 
                           >= [1 1] x + [1 0] y + [11]
                              [0 1]     [0 1]     [6] 
                           =  *(+(x,a()),y)           
        
* Step 3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(*(x,y),z) -> *(x,*(y,z))
            +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
        - Signature:
            {*/2,+/2} / {a/0}
        - Obligation:
            innermost derivational complexity wrt. signature {*,+,a}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))