/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) -> a()
            f(g(x),y) -> f(x,y)
        - Signature:
            {f/2} / {a/0,g/1}
        - Obligation:
             derivational complexity wrt. signature {a,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(a) = [0]                  
          p(f) = [1] x1 + [1] x2 + [6]
          p(g) = [1] x1 + [0]         
        
        Following rules are strictly oriented:
        f(x,x) = [2] x + [6]
               > [0]        
               = a()        
        
        
        Following rules are (at-least) weakly oriented:
        f(g(x),y) =  [1] x + [1] y + [6]
                  >= [1] x + [1] y + [6]
                  =  f(x,y)             
        
* Step 2: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(g(x),y) -> f(x,y)
        - Weak TRS:
            f(x,x) -> a()
        - Signature:
            {f/2} / {a/0,g/1}
        - Obligation:
             derivational complexity wrt. signature {a,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(a) = [0]                  
          p(f) = [1] x1 + [1] x2 + [2]
          p(g) = [1] x1 + [11]        
        
        Following rules are strictly oriented:
        f(g(x),y) = [1] x + [1] y + [13]
                  > [1] x + [1] y + [2] 
                  = f(x,y)              
        
        
        Following rules are (at-least) weakly oriented:
        f(x,x) =  [2] x + [2]
               >= [0]        
               =  a()        
        
* Step 3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(x,x) -> a()
            f(g(x),y) -> f(x,y)
        - Signature:
            {f/2} / {a/0,g/1}
        - Obligation:
             derivational complexity wrt. signature {a,f,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))