/export/starexec/sandbox2/solver/bin/starexec_run_tct_dc /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:
            f(x,x,y) -> x
            f(x,y,y) -> y
            f(x,y,g(y)) -> x
            f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
            f(g(x),x,y) -> y
        - Signature:
            {f/3} / {g/1}
        - Obligation:
             derivational complexity wrt. signature {f,g}
    + 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(f) = [1] x1 + [1] x2 + [1] x3 + [7]
          p(g) = [1] x1 + [0]                  
        
        Following rules are strictly oriented:
                      f(x,x,y) = [2] x + [1] y + [7]                         
                               > [1] x + [0]                                 
                               = x                                           
        
                      f(x,y,y) = [1] x + [2] y + [7]                         
                               > [1] y + [0]                                 
                               = y                                           
        
                   f(x,y,g(y)) = [1] x + [2] y + [7]                         
                               > [1] x + [0]                                 
                               = x                                           
        
        f(f(x,y,z),u,f(x,y,v)) = [1] u + [1] v + [2] x + [2] y + [1] z + [21]
                               > [1] u + [1] v + [1] x + [1] y + [1] z + [14]
                               = f(x,y,f(z,u,v))                             
        
                   f(g(x),x,y) = [2] x + [1] y + [7]                         
                               > [1] y + [0]                                 
                               = y                                           
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(x,x,y) -> x
            f(x,y,y) -> y
            f(x,y,g(y)) -> x
            f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
            f(g(x),x,y) -> y
        - Signature:
            {f/3} / {g/1}
        - Obligation:
             derivational complexity wrt. signature {f,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))