/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:
 f(x,y) -> g(x,y)
 g(h(x),y) -> h(f(x,y))
 g(h(x),y) -> h(g(x,y))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                  [0]
   [h](x0) = x0 + [1]
                  [1],
   
                 [1 0 1]     [1 0 0]  
   [g](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                 [0 1 0]     [0 0 0]  ,
   
                 [1 0 1]     [1 0 0]     [1]
   [f](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                 [0 1 0]     [0 0 0]     [0]
  orientation:
            [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]          
   f(x,y) = [0 1 0]x + [0 0 0]y + [0] >= [0 1 0]x + [0 0 0]y = g(x,y)
            [0 1 0]    [0 0 0]    [0]    [0 1 0]    [0 0 0]          
   
               [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]    [1]            
   g(h(x),y) = [0 1 0]x + [0 0 0]y + [1] >= [0 1 0]x + [0 0 0]y + [1] = h(f(x,y))
               [0 1 0]    [0 0 0]    [1]    [0 1 0]    [0 0 0]    [1]            
   
               [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]    [0]            
   g(h(x),y) = [0 1 0]x + [0 0 0]y + [1] >= [0 1 0]x + [0 0 0]y + [1] = h(g(x,y))
               [0 1 0]    [0 0 0]    [1]    [0 1 0]    [0 0 0]    [1]            
  problem:
   g(h(x),y) -> h(f(x,y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [h](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                  [1 0 0]     [1 0 0]     [1]
    [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                  [0 0 0]     [0 0 0]     [0],
    
                  [1 0 0]     [1 0 0]  
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  
   orientation:
                [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]             
    g(h(x),y) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y = h(f(x,y))
                [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]             
   problem:
    
   Qed