/export/starexec/sandbox2/solver/bin/starexec_run_tct_dci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^2))
* Step 1: NaturalMI.  WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,x) -> x
            *(x,*(y,z)) -> *(*(x,y),z)
        - Signature:
            {*/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]
        
        Following rules are strictly oriented:
        *(x,x) = [2] x + [3]
               > [1] x + [0]
               = x          
        
        
        Following rules are (at-least) weakly oriented:
        *(x,*(y,z)) =  [1] x + [1] y + [1] z + [6]
                    >= [1] x + [1] y + [1] z + [6]
                    =  *(*(x,y),z)                
        
* Step 2: NaturalMI.  WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,*(y,z)) -> *(*(x,y),z)
        - Weak TRS:
            *(x,x) -> x
        - Signature:
            {*/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 0] x1 + [1 15] x2 + [4]
                 [0 1]      [0  1]      [1]
        
        Following rules are strictly oriented:
        *(x,*(y,z)) = [1 0] x + [1 15] y + [1 30] z + [23]
                      [0 1]     [0  1]     [0  1]     [2] 
                    > [1 0] x + [1 15] y + [1 15] z + [8] 
                      [0 1]     [0  1]     [0  1]     [2] 
                    = *(*(x,y),z)                         
        
        
        Following rules are (at-least) weakly oriented:
        *(x,x) =  [2 15] x + [4]
                  [0  2]     [1]
               >= [1 0] x + [0] 
                  [0 1]     [0] 
               =  x             
        
* Step 3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,x) -> x
            *(x,*(y,z)) -> *(*(x,y),z)
        - Signature:
            {*/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))