/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

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