/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:
 flatten(nil()) -> nil()
 flatten(unit(x)) -> flatten(x)
 flatten(++(x,y)) -> ++(flatten(x),flatten(y))
 flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
 flatten(flatten(x)) -> flatten(x)
 rev(nil()) -> nil()
 rev(unit(x)) -> unit(x)
 rev(++(x,y)) -> ++(rev(y),rev(x))
 rev(rev(x)) -> x
 ++(x,nil()) -> x
 ++(nil(),y) -> y
 ++(++(x,y),z) -> ++(x,++(y,z))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [rev](x0) = 2x0,
   
   [++](x0, x1) = x0 + x1 + 5,
   
   [unit](x0) = x0,
   
   [flatten](x0) = 4x0 + 6,
   
   [nil] = 0
  orientation:
   flatten(nil()) = 6 >= 0 = nil()
   
   flatten(unit(x)) = 4x + 6 >= 4x + 6 = flatten(x)
   
   flatten(++(x,y)) = 4x + 4y + 26 >= 4x + 4y + 17 = ++(flatten(x),flatten(y))
   
   flatten(++(unit(x),y)) = 4x + 4y + 26 >= 4x + 4y + 17 = ++(flatten(x),flatten(y))
   
   flatten(flatten(x)) = 16x + 30 >= 4x + 6 = flatten(x)
   
   rev(nil()) = 0 >= 0 = nil()
   
   rev(unit(x)) = 2x >= x = unit(x)
   
   rev(++(x,y)) = 2x + 2y + 10 >= 2x + 2y + 5 = ++(rev(y),rev(x))
   
   rev(rev(x)) = 4x >= x = x
   
   ++(x,nil()) = x + 5 >= x = x
   
   ++(nil(),y) = y + 5 >= y = y
   
   ++(++(x,y),z) = x + y + z + 10 >= x + y + z + 10 = ++(x,++(y,z))
  problem:
   flatten(unit(x)) -> flatten(x)
   rev(nil()) -> nil()
   rev(unit(x)) -> unit(x)
   rev(rev(x)) -> x
   ++(++(x,y),z) -> ++(x,++(y,z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  
    [rev](x0) = x0
                  ,
    
                   [1 0 0]     [1 0 0]  
    [++](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                   [0 0 1]     [0 0 0]  ,
    
                 [1 0 1]     [1]
    [unit](x0) = [1 0 0]x0 + [0]
                 [0 1 0]     [0],
    
                    [1 0 0]  
    [flatten](x0) = [0 0 0]x0
                    [0 0 0]  ,
    
            [1]
    [nil] = [0]
            [0]
   orientation:
                       [1 0 1]    [1]    [1 0 0]              
    flatten(unit(x)) = [0 0 0]x + [0] >= [0 0 0]x = flatten(x)
                       [0 0 0]    [0]    [0 0 0]              
    
                 [1]    [1]        
    rev(nil()) = [0] >= [0] = nil()
                 [0]    [0]        
    
                   [1 0 1]    [1]    [1 0 1]    [1]          
    rev(unit(x)) = [1 0 0]x + [0] >= [1 0 0]x + [0] = unit(x)
                   [0 1 0]    [0]    [0 1 0]    [0]          
    
                            
    rev(rev(x)) = x >= x = x
                            
    
                    [1 0 0]    [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]    [1 0 0]                 
    ++(++(x,y),z) = [0 0 1]x + [0 0 0]y + [0 0 0]z >= [0 0 1]x + [0 0 0]y + [0 0 0]z = ++(x,++(y,z))
                    [0 0 1]    [0 0 0]    [0 0 0]     [0 0 1]    [0 0 0]    [0 0 0]                 
   problem:
    rev(nil()) -> nil()
    rev(unit(x)) -> unit(x)
    rev(rev(x)) -> x
    ++(++(x,y),z) -> ++(x,++(y,z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [rev](x0) = 2x0 + 1,
     
     [++](x0, x1) = x0 + x1,
     
     [unit](x0) = x0 + 1,
     
     [nil] = 0
    orientation:
     rev(nil()) = 1 >= 0 = nil()
     
     rev(unit(x)) = 2x + 3 >= x + 1 = unit(x)
     
     rev(rev(x)) = 4x + 3 >= x = x
     
     ++(++(x,y),z) = x + y + z >= x + y + z = ++(x,++(y,z))
    problem:
     ++(++(x,y),z) -> ++(x,++(y,z))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [++](x0, x1) = 2x0 + x1 + 1
     orientation:
      ++(++(x,y),z) = 4x + 2y + z + 3 >= 2x + 2y + z + 2 = ++(x,++(y,z))
     problem:
      
     Qed