/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(f(x)) -> f(c(f(x)))
 f(f(x)) -> f(d(f(x)))
 g(c(x)) -> x
 g(d(x)) -> x
 g(c(h(0()))) -> g(d(1()))
 g(c(1())) -> g(d(h(0())))
 g(h(x)) -> g(x)

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