/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:
 rev(nil()) -> nil()
 rev(.(x,y)) -> ++(rev(y),.(x,nil()))
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(nil()) -> true()
 null(.(x,y)) -> false()
 ++(nil(),y) -> y
 ++(.(x,y),z) -> .(x,++(y,z))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [0]
   [false] = [0]
             [0],
   
            [0]
   [true] = [0]
            [0],
   
                [1 0 0]  
   [null](x0) = [1 0 0]x0
                [0 0 0]  ,
   
                 
   [cdr](x0) = x0
                 ,
   
               [1 0 0]  
   [car](x0) = [0 0 1]x0
               [0 0 1]  ,
   
                         
   [++](x0, x1) = x0 + x1
                         ,
   
                 [1 0 0]          [0]
   [.](x0, x1) = [0 0 0]x0 + x1 + [1]
                 [0 1 1]          [0],
   
               [1 1 1]  
   [rev](x0) = [0 1 0]x0
               [0 1 1]  ,
   
           [0]
   [nil] = [0]
           [1]
  orientation:
                [1]    [0]        
   rev(nil()) = [0] >= [0] = nil()
                [1]    [1]        
   
                 [1 1 1]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [0]                        
   rev(.(x,y)) = [0 0 0]x + [0 1 0]y + [1] >= [0 0 0]x + [0 1 0]y + [1] = ++(rev(y),.(x,nil()))
                 [0 1 1]    [0 1 1]    [1]    [0 1 1]    [0 1 1]    [1]                        
   
                 [1 0 0]    [1 0 0]          
   car(.(x,y)) = [0 1 1]x + [0 0 1]y >= x = x
                 [0 1 1]    [0 0 1]          
   
                 [1 0 0]        [0]         
   cdr(.(x,y)) = [0 0 0]x + y + [1] >= y = y
                 [0 1 1]        [0]         
   
                 [0]    [0]         
   null(nil()) = [0] >= [0] = true()
                 [0]    [0]         
   
                  [1 0 0]    [1 0 0]     [0]          
   null(.(x,y)) = [1 0 0]x + [1 0 0]y >= [0] = false()
                  [0 0 0]    [0 0 0]     [0]          
   
                     [0]         
   ++(nil(),y) = y + [0] >= y = y
                     [1]         
   
                  [1 0 0]            [0]    [1 0 0]            [0]               
   ++(.(x,y),z) = [0 0 0]x + y + z + [1] >= [0 0 0]x + y + z + [1] = .(x,++(y,z))
                  [0 1 1]            [0]    [0 1 1]            [0]               
  problem:
   car(.(x,y)) -> x
   cdr(.(x,y)) -> y
   null(nil()) -> true()
   null(.(x,y)) -> false()
   ++(nil(),y) -> y
   ++(.(x,y),z) -> .(x,++(y,z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [0]
    [false] = [0]
              [0],
    
             [0]
    [true] = [0]
             [0],
    
                 [1 0 0]     [1]
    [null](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
                  
    [cdr](x0) = x0
                  ,
    
                [1 0 0]     [1]
    [car](x0) = [0 0 1]x0 + [0]
                [0 0 1]     [0],
    
                   [1 1 0]       
    [++](x0, x1) = [0 1 0]x0 + x1
                   [0 0 1]       ,
    
                  [1 0 1]          [0]
    [.](x0, x1) = [0 0 0]x0 + x1 + [1]
                  [0 1 1]          [0],
    
            [0]
    [nil] = [0]
            [0]
   orientation:
                  [1 0 1]    [1 0 0]    [1]         
    car(.(x,y)) = [0 1 1]x + [0 0 1]y + [0] >= x = x
                  [0 1 1]    [0 0 1]    [0]         
    
                  [1 0 1]        [0]         
    cdr(.(x,y)) = [0 0 0]x + y + [1] >= y = y
                  [0 1 1]        [0]         
    
                  [1]    [0]         
    null(nil()) = [0] >= [0] = true()
                  [0]    [0]         
    
                   [1 0 1]    [1 0 0]    [1]    [0]          
    null(.(x,y)) = [0 0 0]x + [0 0 0]y + [0] >= [0] = false()
                   [0 0 0]    [0 0 0]    [0]    [0]          
    
                            
    ++(nil(),y) = y >= y = y
                            
    
                   [1 0 1]    [1 1 0]        [1]    [1 0 1]    [1 1 0]        [0]               
    ++(.(x,y),z) = [0 0 0]x + [0 1 0]y + z + [1] >= [0 0 0]x + [0 1 0]y + z + [1] = .(x,++(y,z))
                   [0 1 1]    [0 0 1]        [0]    [0 1 1]    [0 0 1]        [0]               
   problem:
    cdr(.(x,y)) -> y
    ++(nil(),y) -> y
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 1 0]  
     [cdr](x0) = [0 0 1]x0
                 [1 0 0]  ,
     
                    [1 0 0]       
     [++](x0, x1) = [0 0 0]x0 + x1
                    [0 0 0]       ,
     
                   [1 0 1]     [1 0 1]     [0]
     [.](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1]
                   [0 0 0]     [0 1 0]     [0],
     
             [0]
     [nil] = [0]
             [0]
    orientation:
                   [1 0 1]    [1 1 1]    [1]         
     cdr(.(x,y)) = [0 0 0]x + [0 1 0]y + [0] >= y = y
                   [1 0 1]    [1 0 1]    [0]         
     
                             
     ++(nil(),y) = y >= y = y
                             
    problem:
     ++(nil(),y) -> y
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                     [1 1 0]       
      [++](x0, x1) = [0 0 0]x0 + x1
                     [0 0 0]       ,
      
              [0]
      [nil] = [1]
              [0]
     orientation:
                        [1]         
      ++(nil(),y) = y + [0] >= y = y
                        [0]         
     problem:
      
     Qed