/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:
 f(g(x)) -> f(a(g(g(f(x))),g(f(x))))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 1 1]  
   [f](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 1 0]     [0]
   [g](x0) = [0 1 1]x0 + [1]
             [1 0 1]     [1],
   
                 [1 0 0]     [1 0 0]  
   [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  
  orientation:
             [2 2 2]    [2]    [2 2 2]    [1]                           
   f(g(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(a(g(g(f(x))),g(f(x))))
             [0 0 0]    [0]    [0 0 0]    [0]                           
  problem:
   
  Qed