/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 a__f(f(a())) -> a__f(g(f(a())))
 mark(f(X)) -> a__f(mark(X))
 mark(a()) -> a()
 mark(g(X)) -> g(X)
 a__f(X) -> f(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 0 0]  
   [mark](x0) = [0 1 0]x0
                [0 1 0]  ,
   
             [1 1 0]     [0]
   [f](x0) = [0 0 0]x0 + [1]
             [0 0 0]     [1],
   
             [1 0 0]  
   [g](x0) = [1 0 0]x0
             [0 0 0]  ,
   
         [0]
   [a] = [0]
         [0],
   
                [1 1 0]     [0]
   [a__f](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1]
  orientation:
                  [1]    [0]                  
   a__f(f(a())) = [1] >= [1] = a__f(g(f(a())))
                  [1]    [1]                  
   
                [1 1 0]    [0]    [1 1 0]    [0]                
   mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__f(mark(X))
                [0 0 0]    [1]    [0 0 0]    [1]                
   
               [0]    [0]      
   mark(a()) = [0] >= [0] = a()
               [0]    [0]      
   
                [1 0 0]     [1 0 0]        
   mark(g(X)) = [1 0 0]X >= [1 0 0]X = g(X)
                [1 0 0]     [0 0 0]        
   
             [1 1 0]    [0]    [1 1 0]    [0]       
   a__f(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
             [0 0 0]    [1]    [0 0 0]    [1]       
  problem:
   mark(f(X)) -> a__f(mark(X))
   mark(a()) -> a()
   mark(g(X)) -> g(X)
   a__f(X) -> f(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark](x0) = 5x0 + 4,
    
    [f](x0) = x0,
    
    [g](x0) = 2x0,
    
    [a] = 4,
    
    [a__f](x0) = x0
   orientation:
    mark(f(X)) = 5X + 4 >= 5X + 4 = a__f(mark(X))
    
    mark(a()) = 24 >= 4 = a()
    
    mark(g(X)) = 10X + 4 >= 2X = g(X)
    
    a__f(X) = X >= X = f(X)
   problem:
    mark(f(X)) -> a__f(mark(X))
    a__f(X) -> f(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 1 0]     [0]
     [mark](x0) = [1 1 0]x0 + [0]
                  [0 0 0]     [1],
     
                    [0]
     [f](x0) = x0 + [1]
                    [0],
     
                       [0]
     [a__f](x0) = x0 + [1]
                       [0]
    orientation:
                  [1 1 0]    [1]    [1 1 0]    [0]                
     mark(f(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = a__f(mark(X))
                  [0 0 0]    [1]    [0 0 0]    [1]                
     
                   [0]        [0]       
     a__f(X) = X + [1] >= X + [1] = f(X)
                   [0]        [0]       
    problem:
     a__f(X) -> f(X)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]  
      [f](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                   [1 0 0]     [1]
      [a__f](x0) = [0 0 0]x0 + [0]
                   [0 0 1]     [0]
     orientation:
                [1 0 0]    [1]    [1 0 0]        
      a__f(X) = [0 0 0]X + [0] >= [0 0 0]X = f(X)
                [0 0 1]    [0]    [0 0 0]        
     problem:
      
     Qed