/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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,
   
   [flatten](x0) = x0,
   
   [++](x0, x1) = x0 + x1 + 4,
   
   [nil] = 3,
   
   [unit](x0) = x0
  orientation:
   flatten(nil()) = 3 >= 3 = nil()
   
   flatten(unit(x)) = x >= x = flatten(x)
   
   flatten(++(x,y)) = x + y + 4 >= x + y + 4 = ++(flatten(x),flatten(y))
   
   flatten(++(unit(x),y)) = x + y + 4 >= x + y + 4 = ++(flatten(x),flatten(y))
   
   flatten(flatten(x)) = x >= x = flatten(x)
   
   rev(nil()) = 6 >= 3 = nil()
   
   rev(unit(x)) = 2x >= x = unit(x)
   
   rev(++(x,y)) = 2x + 2y + 8 >= 2x + 2y + 4 = ++(rev(y),rev(x))
   
   rev(rev(x)) = 4x >= x = x
   
   ++(x,nil()) = x + 7 >= x = x
   
   ++(nil(),y) = y + 7 >= y = y
   
   ++(++(x,y),z) = x + y + z + 8 >= x + y + z + 8 = ++(x,++(y,z))
  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(unit(x)) -> unit(x)
   rev(rev(x)) -> x
   ++(++(x,y),z) -> ++(x,++(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [rev](x0) = 2x0 + 3,
    
    [flatten](x0) = x0,
    
    [++](x0, x1) = 4x0 + x1 + 2,
    
    [nil] = 4,
    
    [unit](x0) = x0
   orientation:
    flatten(nil()) = 4 >= 4 = nil()
    
    flatten(unit(x)) = x >= x = flatten(x)
    
    flatten(++(x,y)) = 4x + y + 2 >= 4x + y + 2 = ++(flatten(x),flatten(y))
    
    flatten(++(unit(x),y)) = 4x + y + 2 >= 4x + y + 2 = ++(flatten(x),flatten(y))
    
    flatten(flatten(x)) = x >= x = flatten(x)
    
    rev(unit(x)) = 2x + 3 >= x = unit(x)
    
    rev(rev(x)) = 4x + 9 >= x = x
    
    ++(++(x,y),z) = 16x + 4y + z + 10 >= 4x + 4y + z + 4 = ++(x,++(y,z))
   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)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [flatten](x0) = 2x0 + 1,
     
     [++](x0, x1) = x0 + 2x1 + 2,
     
     [nil] = 0,
     
     [unit](x0) = 6x0 + 1
    orientation:
     flatten(nil()) = 1 >= 0 = nil()
     
     flatten(unit(x)) = 12x + 3 >= 2x + 1 = flatten(x)
     
     flatten(++(x,y)) = 2x + 4y + 5 >= 2x + 4y + 5 = ++(flatten(x),flatten(y))
     
     flatten(++(unit(x),y)) = 12x + 4y + 7 >= 2x + 4y + 5 = ++(flatten(x),flatten(y))
     
     flatten(flatten(x)) = 4x + 3 >= 2x + 1 = flatten(x)
    problem:
     flatten(++(x,y)) -> ++(flatten(x),flatten(y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                      [1 1 1]  
      [flatten](x0) = [0 1 0]x0
                      [0 0 1]  ,
      
                          [1 0 0]     [0]
      [++](x0, x1) = x0 + [0 1 1]x1 + [0]
                          [0 0 0]     [1]
     orientation:
                         [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [0]                            
      flatten(++(x,y)) = [0 1 0]x + [0 1 1]y + [0] >= [0 1 0]x + [0 1 1]y + [0] = ++(flatten(x),flatten(y))
                         [0 0 1]    [0 0 0]    [1]    [0 0 1]    [0 0 0]    [1]                            
     problem:
      
     Qed