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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [k](x0, x1, x2) = 4x0 + 4x1 + x2 + 1,
   
   [g](x0) = x0,
   
   [h](x0) = 4x0,
   
   [f](x0) = x0,
   
   [a] = 0
  orientation:
   f(a()) = 0 >= 0 = g(h(a()))
   
   h(g(x)) = 4x >= 4x = g(h(f(x)))
   
   k(x,h(x),a()) = 20x + 1 >= 4x = h(x)
   
   k(f(x),y,x) = 5x + 4y + 1 >= x = f(x)
  problem:
   f(a()) -> g(h(a()))
   h(g(x)) -> g(h(f(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 1 0]     [0]
    [g](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
              [1 0 1]     [0]
    [h](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
              [1 1 0]     [0]
    [f](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
          [0]
    [a] = [1]
          [0]
   orientation:
             [1]    [0]            
    f(a()) = [0] >= [0] = g(h(a()))
             [1]    [1]            
    
              [1 1 0]    [1]    [1 1 0]    [1]             
    h(g(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = g(h(f(x)))
              [0 0 0]    [1]    [0 0 0]    [1]             
   problem:
    h(g(x)) -> g(h(f(x)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [0]
     [g](x0) = [0 0 0]x0 + [1]
               [0 0 1]     [0],
     
               [1 1 0]     [0]
     [h](x0) = [0 0 0]x0 + [1]
               [1 0 0]     [0],
     
               [1 0 0]  
     [f](x0) = [0 0 0]x0
               [0 0 0]  
    orientation:
               [1 0 0]    [1]    [1 0 0]    [0]             
     h(g(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = g(h(f(x)))
               [1 0 0]    [0]    [1 0 0]    [0]             
    problem:
     
    Qed