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


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YES

Problem:
 strict:
  f(g(x),y,z) -> f(x,y,g(z))
 weak:
  f(x,y,g(z)) -> f(x,g(y),z)
  f(x,a(),z) -> f(x,g(a()),z)
  f(x,y,z) -> f(x,y,g(z))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                     [1 1]     [2 0]     [1 0]  
   [f](x0, x1, x2) = [0 1]x0 + [0 0]x1 + [2 0]x2,
   
             [1 0]     [0]
   [g](x0) = [0 2]x0 + [2],
   
         [0]
   [a] = [0]
  orientation:
                 [1 2]    [2 0]    [1 0]    [2]    [1 1]    [2 0]    [1 0]               
   f(g(x),y,z) = [0 2]x + [0 0]y + [2 0]z + [2] >= [0 1]x + [0 0]y + [2 0]z = f(x,y,g(z))
   
                 [1 1]    [2 0]    [1 0]     [1 1]    [2 0]    [1 0]               
   f(x,y,g(z)) = [0 1]x + [0 0]y + [2 0]z >= [0 1]x + [0 0]y + [2 0]z = f(x,g(y),z)
   
                [1 1]    [1 0]     [1 1]    [1 0]                 
   f(x,a(),z) = [0 1]x + [2 0]z >= [0 1]x + [2 0]z = f(x,g(a()),z)
   
              [1 1]    [2 0]    [1 0]     [1 1]    [2 0]    [1 0]               
   f(x,y,z) = [0 1]x + [0 0]y + [2 0]z >= [0 1]x + [0 0]y + [2 0]z = f(x,y,g(z))
  problem:
   strict:
    
   weak:
    f(x,y,g(z)) -> f(x,g(y),z)
    f(x,a(),z) -> f(x,g(a()),z)
    f(x,y,z) -> f(x,y,g(z))
  Qed