/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:
 merge(x,nil()) -> x
 merge(nil(),y) -> y
 merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
 merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
         [0]
   [v] = [0]
         [0],
   
         [0]
   [u] = [0]
         [1],
   
                  [1 0 0]     [1 0 0]  
   [++](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                  [0 0 1]     [0 0 0]  ,
   
                               [0]
   [merge](x0, x1) = x0 + x1 + [1]
                               [0],
   
           [1]
   [nil] = [0]
           [0]
  orientation:
                        [1]         
   merge(x,nil()) = x + [1] >= x = x
                        [0]         
   
                        [1]         
   merge(nil(),y) = y + [1] >= y = y
                        [0]         
   
                                [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [0]                             
   merge(++(x,y),++(u(),v())) = [0 0 0]x + [0 1 0]y + [1] >= [0 0 0]x + [0 1 0]y + [1] = ++(x,merge(y,++(u(),v())))
                                [0 0 1]    [0 0 0]    [1]    [0 0 1]    [0 0 0]    [0]                             
   
                                [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [0]                             
   merge(++(x,y),++(u(),v())) = [0 0 0]x + [0 1 0]y + [1] >= [0 0 0]x + [0 1 0]y + [1] = ++(u(),merge(++(x,y),v()))
                                [0 0 1]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]                             
  problem:
   merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
   merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [v] = 0,
    
    [u] = 1,
    
    [++](x0, x1) = x0 + x1,
    
    [merge](x0, x1) = 2x0 + 4x1
   orientation:
    merge(++(x,y),++(u(),v())) = 2x + 2y + 4 >= x + 2y + 4 = ++(x,merge(y,++(u(),v())))
    
    merge(++(x,y),++(u(),v())) = 2x + 2y + 4 >= 2x + 2y + 1 = ++(u(),merge(++(x,y),v()))
   problem:
    merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [v] = [0]
           [0],
     
           [0]
     [u] = [0]
           [0],
     
                    [1 1 0]          [0]
     [++](x0, x1) = [0 0 0]x0 + x1 + [1]
                    [0 0 0]          [1],
     
                       [1 0 1]     [1 0 0]  
     [merge](x0, x1) = [1 0 1]x0 + [0 0 0]x1
                       [0 1 0]     [0 0 0]  
    orientation:
                                  [1 1 0]    [1 0 1]    [1]    [1 1 0]    [1 0 1]    [0]                             
     merge(++(x,y),++(u(),v())) = [1 1 0]x + [1 0 1]y + [1] >= [0 0 0]x + [1 0 1]y + [1] = ++(x,merge(y,++(u(),v())))
                                  [0 0 0]    [0 1 0]    [1]    [0 0 0]    [0 1 0]    [1]                             
    problem:
     
    Qed