/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),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:
   [g](x0, x1) = x0 + 2x1,
   
   [f](x0, x1) = 2x0 + x1 + 1,
   
   [h](x0, x1) = x0 + 4x1 + 4
  orientation:
   g(f(x,y),z) = 2x + y + 2z + 1 >= 2x + y + 2z + 1 = f(x,g(y,z))
   
   g(h(x,y),z) = x + 4y + 2z + 4 >= x + 4y + 2z + 2 = g(x,f(y,z))
   
   g(x,h(y,z)) = x + 2y + 8z + 8 >= x + 2y + 4z + 4 = h(g(x,y),z)
  problem:
   g(f(x,y),z) -> f(x,g(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0, x1) = 6x0 + x1 + 1,
    
    [f](x0, x1) = 3x0 + x1 + 4
   orientation:
    g(f(x,y),z) = 18x + 6y + z + 25 >= 3x + 6y + z + 5 = f(x,g(y,z))
   problem:
    
   Qed