/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(X) -> if(X,c(),n__f(true()))
 if(true(),X,Y) -> X
 if(false(),X,Y) -> activate(Y)
 f(X) -> n__f(X)
 activate(n__f(X)) -> f(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 0 0]     [1]
   [activate](x0) = [1 1 0]x0 + [0]
                    [0 0 1]     [1],
   
             [1]
   [false] = [1]
             [0],
   
                      [1 0 0]          [1 0 0]  
   [if](x0, x1, x2) = [0 0 0]x0 + x1 + [1 1 0]x2
                      [0 1 0]          [0 0 1]  ,
   
                [1 0 0]     [0]
   [n__f](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0],
   
            [0]
   [true] = [1]
            [0],
   
         [0]
   [c] = [0]
         [0],
   
             [1 0 0]     [1]
   [f](x0) = [0 0 0]x0 + [1]
             [0 1 0]     [1]
  orientation:
          [1 0 0]    [1]    [1 0 0]    [0]                         
   f(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = if(X,c(),n__f(true()))
          [0 1 0]    [1]    [0 1 0]    [1]                         
   
                        [1 0 0]    [0]         
   if(true(),X,Y) = X + [1 1 0]Y + [0] >= X = X
                        [0 0 1]    [1]         
   
                         [1 0 0]    [1]    [1 0 0]    [1]              
   if(false(),X,Y) = X + [1 1 0]Y + [0] >= [1 1 0]Y + [0] = activate(Y)
                         [0 0 1]    [1]    [0 0 1]    [1]              
   
          [1 0 0]    [1]    [1 0 0]    [0]          
   f(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = n__f(X)
          [0 1 0]    [1]    [0 1 0]    [0]          
   
                       [1 0 0]    [1]    [1 0 0]    [1]       
   activate(n__f(X)) = [1 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
                       [0 1 0]    [1]    [0 1 0]    [1]       
   
                 [1 0 0]    [1]         
   activate(X) = [1 1 0]X + [0] >= X = X
                 [0 0 1]    [1]         
  problem:
   if(true(),X,Y) -> X
   if(false(),X,Y) -> activate(Y)
   activate(n__f(X)) -> f(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]  
    [activate](x0) = [0 0 0]x0
                     [0 0 0]  ,
    
              [0]
    [false] = [0]
              [0],
    
                       [1 0 0]          [1 0 0]     [1]
    [if](x0, x1, x2) = [0 0 0]x0 + x1 + [0 0 0]x2 + [0]
                       [0 0 1]          [0 0 0]     [0],
    
                 [1 0 0]     [1]
    [n__f](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
             [0]
    [true] = [0]
             [1],
    
              [1 0 0]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
                         [1 0 0]    [1]         
    if(true(),X,Y) = X + [0 0 0]Y + [0] >= X = X
                         [0 0 0]    [1]         
    
                          [1 0 0]    [1]    [1 0 0]               
    if(false(),X,Y) = X + [0 0 0]Y + [0] >= [0 0 0]Y = activate(Y)
                          [0 0 0]    [0]    [0 0 0]               
    
                        [1 0 0]    [1]    [1 0 0]        
    activate(n__f(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(X)
                        [0 0 0]    [0]    [0 0 0]        
   problem:
    
   Qed