/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0, x1) = 4x0 + x1,
   
   [f](x0) = x0 + 2,
   
   [h](x0, x1) = 4x0 + x1 + 6
  orientation:
   g(f(x),y) = 4x + y + 8 >= 4x + y + 8 = f(h(x,y))
   
   h(x,y) = 4x + y + 6 >= 4x + y + 2 = g(x,f(y))
  problem:
   g(f(x),y) -> f(h(x,y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1 0 0]     [1]
    [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                  [0 0 0]     [0 0 0]     [0],
    
              [1 0 0]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                  [1 0 0]     [1 0 0]  
    [h](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(f(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = f(h(x,y))
                [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]             
   problem:
    
   Qed