/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(.(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:
               [1 0 0]     [1]
   [car](x0) = [1 0 0]x0 + [0]
               [1 0 0]     [0],
   
             [0]
   [false] = [0]
             [0],
   
               [1 0 0]     [1]
   [rev](x0) = [0 0 0]x0 + [1]
               [1 0 0]     [1],
   
                  [1 0 0]     [1 1 0]     [0]
   [++](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0]
                  [0 0 0]     [0 0 1]     [1],
   
                    [1]
   [cdr](x0) = x0 + [0]
                    [0],
   
           [0]
   [nil] = [0]
           [0],
   
            [0]
   [true] = [0]
            [0],
   
                [1 0 0]  
   [null](x0) = [0 0 1]x0
                [0 1 0]  ,
   
                 [1 1 1]       
   [.](x0, x1) = [0 0 0]x0 + x1
                 [0 0 0]       
  orientation:
                [1]    [0]        
   rev(nil()) = [1] >= [0] = nil()
                [1]    [0]        
   
                 [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 0 0]    [1]                        
   rev(.(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [0] = ++(rev(y),.(x,nil()))
                 [1 1 1]    [1 0 0]    [1]    [0 0 0]    [0 0 0]    [1]                        
   
                 [1 1 1]    [1 0 0]    [1]         
   car(.(x,y)) = [1 1 1]x + [1 0 0]y + [0] >= x = x
                 [1 1 1]    [1 0 0]    [0]         
   
                 [1 1 1]        [1]         
   cdr(.(x,y)) = [0 0 0]x + y + [0] >= y = y
                 [0 0 0]        [0]         
   
                 [0]    [0]         
   null(nil()) = [0] >= [0] = true()
                 [0]    [0]         
   
                  [1 1 1]    [1 0 0]     [0]          
   null(.(x,y)) = [0 0 0]x + [0 0 1]y >= [0] = false()
                  [0 0 0]    [0 1 0]     [0]          
   
                 [1 1 0]    [0]         
   ++(nil(),y) = [0 1 0]y + [0] >= y = y
                 [0 0 1]    [1]         
   
                  [1 1 1]    [1 0 0]    [1 1 0]    [0]    [1 1 1]    [1 0 0]    [1 1 0]    [0]               
   ++(.(x,y),z) = [0 0 0]x + [0 0 0]y + [0 1 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 1 0]z + [0] = .(x,++(y,z))
                  [0 0 0]    [0 0 0]    [0 0 1]    [1]    [0 0 0]    [0 0 0]    [0 0 1]    [1]               
  problem:
   rev(.(x,y)) -> ++(rev(y),.(x,nil()))
   null(nil()) -> true()
   null(.(x,y)) -> false()
   ++(nil(),y) -> y
   ++(.(x,y),z) -> .(x,++(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [false] = 0,
    
    [rev](x0) = 5x0 + 3,
    
    [++](x0, x1) = x0 + 4x1 + 1,
    
    [nil] = 0,
    
    [true] = 2,
    
    [null](x0) = 4x0 + 2,
    
    [.](x0, x1) = 2x0 + x1 + 5
   orientation:
    rev(.(x,y)) = 10x + 5y + 28 >= 8x + 5y + 24 = ++(rev(y),.(x,nil()))
    
    null(nil()) = 2 >= 2 = true()
    
    null(.(x,y)) = 8x + 4y + 22 >= 0 = false()
    
    ++(nil(),y) = 4y + 1 >= y = y
    
    ++(.(x,y),z) = 2x + y + 4z + 6 >= 2x + y + 4z + 6 = .(x,++(y,z))
   problem:
    null(nil()) -> true()
    ++(.(x,y),z) -> .(x,++(y,z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [++](x0, x1) = x0 + x1,
     
     [nil] = 3,
     
     [true] = 0,
     
     [null](x0) = 4x0,
     
     [.](x0, x1) = x0 + x1 + 4
    orientation:
     null(nil()) = 12 >= 0 = true()
     
     ++(.(x,y),z) = x + y + z + 4 >= x + y + z + 4 = .(x,++(y,z))
    problem:
     ++(.(x,y),z) -> .(x,++(y,z))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [++](x0, x1) = 6x0 + x1 + 1,
      
      [.](x0, x1) = 3x0 + x1 + 4
     orientation:
      ++(.(x,y),z) = 18x + 6y + z + 25 >= 3x + 6y + z + 5 = .(x,++(y,z))
     problem:
      
     Qed