/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 rev(nil()) -> nil()
 rev(rev(x)) -> x
 rev(++(x,y)) -> ++(rev(y),rev(x))
 ++(nil(),y) -> y
 ++(x,nil()) -> x
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(x,++(y,z)) -> ++(++(x,y),z)
 make(x) -> .(x,nil())

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 0 0]     [0]
   [make](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1],
   
               [1 0 1]  
   [rev](x0) = [0 0 1]x0
               [0 1 0]  ,
   
                 [1 0 0]       
   [.](x0, x1) = [0 0 0]x0 + x1
                 [0 0 0]       ,
   
           [0]
   [nil] = [1]
           [1],
   
                         
   [++](x0, x1) = x0 + x1
                         
  orientation:
                [1]    [0]        
   rev(nil()) = [1] >= [1] = nil()
                [1]    [1]        
   
                 [1 1 1]          
   rev(rev(x)) = [0 1 0]x >= x = x
                 [0 0 1]          
   
                  [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                     
   rev(++(x,y)) = [0 0 1]x + [0 0 1]y >= [0 0 1]x + [0 0 1]y = ++(rev(y),rev(x))
                  [0 1 0]    [0 1 0]     [0 1 0]    [0 1 0]                     
   
                     [0]         
   ++(nil(),y) = y + [1] >= y = y
                     [1]         
   
                     [0]         
   ++(x,nil()) = x + [1] >= x = x
                     [1]         
   
                  [1 0 0]             [1 0 0]                        
   ++(.(x,y),z) = [0 0 0]x + y + z >= [0 0 0]x + y + z = .(x,++(y,z))
                  [0 0 0]             [0 0 0]                        
   
                                                         
   ++(x,++(y,z)) = x + y + z >= x + y + z = ++(++(x,y),z)
                                                         
   
             [1 0 0]    [0]    [1 0 0]    [0]             
   make(x) = [0 0 0]x + [1] >= [0 0 0]x + [1] = .(x,nil())
             [0 0 0]    [1]    [0 0 0]    [1]             
  problem:
   rev(rev(x)) -> x
   rev(++(x,y)) -> ++(rev(y),rev(x))
   ++(nil(),y) -> y
   ++(x,nil()) -> x
   ++(.(x,y),z) -> .(x,++(y,z))
   ++(x,++(y,z)) -> ++(++(x,y),z)
   make(x) -> .(x,nil())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]     [1]
    [make](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
                  
    [rev](x0) = x0
                  ,
    
                  [1 0 0]     [1 0 0]  
    [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
            [0]
    [nil] = [0]
            [0],
    
                          
    [++](x0, x1) = x0 + x1
                          
   orientation:
                            
    rev(rev(x)) = x >= x = x
                            
    
                                                     
    rev(++(x,y)) = x + y >= x + y = ++(rev(y),rev(x))
                                                     
    
                            
    ++(nil(),y) = y >= y = y
                            
    
                            
    ++(x,nil()) = x >= x = x
                            
    
                   [1 0 0]    [1 0 0]         [1 0 0]    [1 0 0]    [1 0 0]                
    ++(.(x,y),z) = [0 0 0]x + [0 0 0]y + z >= [0 0 0]x + [0 0 0]y + [0 0 0]z = .(x,++(y,z))
                   [0 0 0]    [0 0 0]         [0 0 0]    [0 0 0]    [0 0 0]                
    
                                                          
    ++(x,++(y,z)) = x + y + z >= x + y + z = ++(++(x,y),z)
                                                          
    
              [1 0 0]    [1]    [1 0 0]              
    make(x) = [0 0 0]x + [0] >= [0 0 0]x = .(x,nil())
              [0 0 0]    [0]    [0 0 0]              
   problem:
    rev(rev(x)) -> x
    rev(++(x,y)) -> ++(rev(y),rev(x))
    ++(nil(),y) -> y
    ++(x,nil()) -> x
    ++(.(x,y),z) -> .(x,++(y,z))
    ++(x,++(y,z)) -> ++(++(x,y),z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [rev](x0) = x0,
     
     [.](x0, x1) = 4x0 + x1,
     
     [nil] = 2,
     
     [++](x0, x1) = x0 + x1
    orientation:
     rev(rev(x)) = x >= x = x
     
     rev(++(x,y)) = x + y >= x + y = ++(rev(y),rev(x))
     
     ++(nil(),y) = y + 2 >= y = y
     
     ++(x,nil()) = x + 2 >= x = x
     
     ++(.(x,y),z) = 4x + y + z >= 4x + y + z = .(x,++(y,z))
     
     ++(x,++(y,z)) = x + y + z >= x + y + z = ++(++(x,y),z)
    problem:
     rev(rev(x)) -> x
     rev(++(x,y)) -> ++(rev(y),rev(x))
     ++(.(x,y),z) -> .(x,++(y,z))
     ++(x,++(y,z)) -> ++(++(x,y),z)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [rev](x0) = 3x0 + 4,
      
      [.](x0, x1) = x0 + x1,
      
      [++](x0, x1) = x0 + x1 + 2
     orientation:
      rev(rev(x)) = 9x + 16 >= x = x
      
      rev(++(x,y)) = 3x + 3y + 10 >= 3x + 3y + 10 = ++(rev(y),rev(x))
      
      ++(.(x,y),z) = x + y + z + 2 >= x + y + z + 2 = .(x,++(y,z))
      
      ++(x,++(y,z)) = x + y + z + 4 >= x + y + z + 4 = ++(++(x,y),z)
     problem:
      rev(++(x,y)) -> ++(rev(y),rev(x))
      ++(.(x,y),z) -> .(x,++(y,z))
      ++(x,++(y,z)) -> ++(++(x,y),z)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [rev](x0) = 4x0 + 2,
       
       [.](x0, x1) = 4x0 + x1,
       
       [++](x0, x1) = x0 + x1 + 1
      orientation:
       rev(++(x,y)) = 4x + 4y + 6 >= 4x + 4y + 5 = ++(rev(y),rev(x))
       
       ++(.(x,y),z) = 4x + y + z + 1 >= 4x + y + z + 1 = .(x,++(y,z))
       
       ++(x,++(y,z)) = x + y + z + 2 >= x + y + z + 2 = ++(++(x,y),z)
      problem:
       ++(.(x,y),z) -> .(x,++(y,z))
       ++(x,++(y,z)) -> ++(++(x,y),z)
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [.](x0, x1) = 4x0 + x1 + 2,
        
        [++](x0, x1) = x0 + 2x1 + 1
       orientation:
        ++(.(x,y),z) = 4x + y + 2z + 3 >= 4x + y + 2z + 3 = .(x,++(y,z))
        
        ++(x,++(y,z)) = x + 2y + 4z + 3 >= x + 2y + 2z + 2 = ++(++(x,y),z)
       problem:
        ++(.(x,y),z) -> .(x,++(y,z))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                       [1 0 0]          [0]
         [.](x0, x1) = [0 0 0]x0 + x1 + [1]
                       [0 0 0]          [0],
         
                        [1 1 0]     [1 0 0]  
         [++](x0, x1) = [0 1 1]x0 + [0 0 0]x1
                        [0 0 0]     [1 0 0]  
        orientation:
                        [1 0 0]    [1 1 0]    [1 0 0]    [1]    [1 0 0]    [1 1 0]    [1 0 0]    [0]               
         ++(.(x,y),z) = [0 0 0]x + [0 1 1]y + [0 0 0]z + [1] >= [0 0 0]x + [0 1 1]y + [0 0 0]z + [1] = .(x,++(y,z))
                        [0 0 0]    [0 0 0]    [1 0 0]    [0]    [0 0 0]    [0 0 0]    [1 0 0]    [0]               
        problem:
         
        Qed