/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:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 f(0()) -> s(0())
 f(s(x)) -> minus(s(x),g(f(x)))
 g(0()) -> 0()
 g(s(x)) -> minus(s(x),f(g(x)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 3x0,
   
   [f](x0) = 4x0 + 6,
   
   [s](x0) = 6x0 + 6,
   
   [minus](x0, x1) = x0 + x1 + 4,
   
   [0] = 0
  orientation:
   minus(x,0()) = x + 4 >= x = x
   
   minus(s(x),s(y)) = 6x + 6y + 16 >= x + y + 4 = minus(x,y)
   
   f(0()) = 6 >= 6 = s(0())
   
   f(s(x)) = 24x + 30 >= 18x + 28 = minus(s(x),g(f(x)))
   
   g(0()) = 0 >= 0 = 0()
   
   g(s(x)) = 18x + 18 >= 18x + 16 = minus(s(x),f(g(x)))
  problem:
   f(0()) -> s(0())
   g(0()) -> 0()
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [1]
    [g](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
              [1 0 0]     [1]
    [f](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 0 0]  ,
    
          [0]
    [0] = [0]
          [0]
   orientation:
             [1]    [0]         
    f(0()) = [0] >= [0] = s(0())
             [0]    [0]         
    
             [1]    [0]      
    g(0()) = [0] >= [0] = 0()
             [0]    [0]      
   problem:
    
   Qed