/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 f(1()) -> f(g(1()))
 f(f(x)) -> f(x)
 g(0()) -> g(f(0()))
 g(g(x)) -> g(x)

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