/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(h(x)) -> f(i(x))
 g(i(x)) -> g(h(x))
 h(a()) -> b()
 i(a()) -> b()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a] = 4,
   
   [f](x0) = x0,
   
   [g](x0) = 2x0,
   
   [b] = 0,
   
   [h](x0) = 2x0 + 6,
   
   [i](x0) = 2x0 + 6
  orientation:
   f(h(x)) = 2x + 6 >= 2x + 6 = f(i(x))
   
   g(i(x)) = 4x + 12 >= 4x + 12 = g(h(x))
   
   h(a()) = 14 >= 0 = b()
   
   i(a()) = 14 >= 0 = b()
  problem:
   f(h(x)) -> f(i(x))
   g(i(x)) -> g(h(x))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 1]  
    [f](x0) = [0 0 1]x0
              [0 0 0]  ,
    
              [1 1 0]     [0]
    [g](x0) = [1 0 0]x0 + [1]
              [1 0 0]     [0],
    
              [1 0 0]     [0]
    [h](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
              [1 0 0]     [0]
    [i](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0]
   orientation:
              [1 0 0]    [1]    [1 0 0]           
    f(h(x)) = [0 0 0]x + [1] >= [0 0 0]x = f(i(x))
              [0 0 0]    [0]    [0 0 0]           
    
              [1 0 0]    [1]    [1 0 0]    [0]          
    g(i(x)) = [1 0 0]x + [1] >= [1 0 0]x + [1] = g(h(x))
              [1 0 0]    [0]    [1 0 0]    [0]          
   problem:
    
   Qed