/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:
 strict:
  f(x) -> x
  g(x) -> x
 weak:
  f(x) -> g(x)
  g(x) -> f(x)

Proof:
 Arctic Interpretation Processor:
  dimension: 4
  interpretation:
             [1  0  -& -&]  
             [0  2  -& -&]  
   [g](x0) = [-& -& 1  0 ]x0
             [0  0  -& 1 ]  ,
   
             [1  0  -& -&]  
             [0  2  -& -&]  
   [f](x0) = [-& -& 1  0 ]x0
             [0  0  -& 1 ]  
  orientation:
          [1  0  -& -&]          
          [0  2  -& -&]          
   f(x) = [-& -& 1  0 ]x >= x = x
          [0  0  -& 1 ]          
   
          [1  0  -& -&]          
          [0  2  -& -&]          
   g(x) = [-& -& 1  0 ]x >= x = x
          [0  0  -& 1 ]          
   
          [1  0  -& -&]     [1  0  -& -&]        
          [0  2  -& -&]     [0  2  -& -&]        
   f(x) = [-& -& 1  0 ]x >= [-& -& 1  0 ]x = g(x)
          [0  0  -& 1 ]     [0  0  -& 1 ]        
   
          [1  0  -& -&]     [1  0  -& -&]        
          [0  2  -& -&]     [0  2  -& -&]        
   g(x) = [-& -& 1  0 ]x >= [-& -& 1  0 ]x = f(x)
          [0  0  -& 1 ]     [0  0  -& 1 ]        
  problem:
   strict:
    
   weak:
    f(x) -> g(x)
    g(x) -> f(x)
  Qed