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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [h](x0, x1) = x0 + 3x1 + 1,
   
   [g](x0, x1) = 5x0 + x1,
   
   [f](x0, x1) = 4x0 + x1 + 5
  orientation:
   g(f(x,y),z) = 20x + 5y + z + 25 >= 4x + 5y + z + 5 = f(x,g(y,z))
   
   g(h(x,y),z) = 5x + 15y + z + 5 >= 5x + 4y + z + 5 = g(x,f(y,z))
   
   g(x,h(y,z)) = 5x + y + 3z + 1 >= 5x + y + 3z + 1 = h(g(x,y),z)
  problem:
   g(h(x,y),z) -> g(x,f(y,z))
   g(x,h(y,z)) -> h(g(x,y),z)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                       [1 1 0]     [0]
    [h](x0, x1) = x0 + [0 0 0]x1 + [0]
                       [0 0 0]     [1],
    
                  [1 0 1]     [1 0 1]  
    [g](x0, x1) = [1 0 0]x0 + [0 1 0]x1
                  [0 0 0]     [0 0 1]  ,
    
                  [1 1 0]       
    [f](x0, x1) = [1 1 0]x0 + x1
                  [0 0 0]       
   orientation:
                  [1 0 1]    [1 1 0]    [1 0 1]    [1]    [1 0 1]    [1 1 0]    [1 0 1]               
    g(h(x,y),z) = [1 0 0]x + [1 1 0]y + [0 1 0]z + [0] >= [1 0 0]x + [1 1 0]y + [0 1 0]z = g(x,f(y,z))
                  [0 0 0]    [0 0 0]    [0 0 1]    [0]    [0 0 0]    [0 0 0]    [0 0 1]               
    
                  [1 0 1]    [1 0 1]    [1 1 0]    [1]    [1 0 1]    [1 0 1]    [1 1 0]    [0]              
    g(x,h(y,z)) = [1 0 0]x + [0 1 0]y + [0 0 0]z + [0] >= [1 0 0]x + [0 1 0]y + [0 0 0]z + [0] = h(g(x,y),z)
                  [0 0 0]    [0 0 1]    [0 0 0]    [1]    [0 0 0]    [0 0 1]    [0 0 0]    [1]              
   problem:
    
   Qed