/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:
 g(0()) -> 0()
 g(s(x)) -> f(g(x))
 f(0()) -> 0()

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