/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:
 active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(2nd(X)) -> 2nd(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(from(X)) -> from(active(X))
 active(s(X)) -> s(active(X))
 2nd(mark(X)) -> mark(2nd(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 from(mark(X)) -> mark(from(X))
 s(mark(X)) -> mark(s(X))
 proper(2nd(X)) -> 2nd(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 proper(s(X)) -> s(proper(X))
 2nd(ok(X)) -> ok(2nd(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 from(ok(X)) -> ok(from(X))
 s(ok(X)) -> ok(s(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [from](x0) = 3x0 + 1,
   
   [top](x0) = 2x0,
   
   [2nd](x0) = 4x0,
   
   [mark](x0) = x0,
   
   [s](x0) = 3x0 + 1,
   
   [cons](x0, x1) = x0 + x1,
   
   [ok](x0) = 6x0 + 3,
   
   [proper](x0) = x0,
   
   [active](x0) = 4x0
  orientation:
   active(2nd(cons(X,cons(Y,Z)))) = 16X + 16Y + 16Z >= Y = mark(Y)
   
   active(from(X)) = 12X + 4 >= 10X + 4 = mark(cons(X,from(s(X))))
   
   active(2nd(X)) = 16X >= 16X = 2nd(active(X))
   
   active(cons(X1,X2)) = 4X1 + 4X2 >= 4X1 + X2 = cons(active(X1),X2)
   
   active(from(X)) = 12X + 4 >= 12X + 1 = from(active(X))
   
   active(s(X)) = 12X + 4 >= 12X + 1 = s(active(X))
   
   2nd(mark(X)) = 4X >= 4X = mark(2nd(X))
   
   cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(cons(X1,X2))
   
   from(mark(X)) = 3X + 1 >= 3X + 1 = mark(from(X))
   
   s(mark(X)) = 3X + 1 >= 3X + 1 = mark(s(X))
   
   proper(2nd(X)) = 4X >= 4X = 2nd(proper(X))
   
   proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2))
   
   proper(from(X)) = 3X + 1 >= 3X + 1 = from(proper(X))
   
   proper(s(X)) = 3X + 1 >= 3X + 1 = s(proper(X))
   
   2nd(ok(X)) = 24X + 12 >= 24X + 3 = ok(2nd(X))
   
   cons(ok(X1),ok(X2)) = 6X1 + 6X2 + 6 >= 6X1 + 6X2 + 3 = ok(cons(X1,X2))
   
   from(ok(X)) = 18X + 10 >= 18X + 9 = ok(from(X))
   
   s(ok(X)) = 18X + 10 >= 18X + 9 = ok(s(X))
   
   top(mark(X)) = 2X >= 2X = top(proper(X))
   
   top(ok(X)) = 12X + 6 >= 8X = top(active(X))
  problem:
   active(2nd(cons(X,cons(Y,Z)))) -> mark(Y)
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(2nd(X)) -> 2nd(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   2nd(mark(X)) -> mark(2nd(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   from(mark(X)) -> mark(from(X))
   s(mark(X)) -> mark(s(X))
   proper(2nd(X)) -> 2nd(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(s(X)) -> s(proper(X))
   top(mark(X)) -> top(proper(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [from](x0) = 2x0 + 6,
    
    [top](x0) = 2x0,
    
    [2nd](x0) = x0,
    
    [mark](x0) = x0,
    
    [s](x0) = x0 + 3,
    
    [cons](x0, x1) = 2x0 + x1 + 2,
    
    [proper](x0) = x0,
    
    [active](x0) = 2x0 + 2
   orientation:
    active(2nd(cons(X,cons(Y,Z)))) = 4X + 4Y + 2Z + 10 >= Y = mark(Y)
    
    active(from(X)) = 4X + 14 >= 4X + 14 = mark(cons(X,from(s(X))))
    
    active(2nd(X)) = 2X + 2 >= 2X + 2 = 2nd(active(X))
    
    active(cons(X1,X2)) = 4X1 + 2X2 + 6 >= 4X1 + X2 + 6 = cons(active(X1),X2)
    
    2nd(mark(X)) = X >= X = mark(2nd(X))
    
    cons(mark(X1),X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = mark(cons(X1,X2))
    
    from(mark(X)) = 2X + 6 >= 2X + 6 = mark(from(X))
    
    s(mark(X)) = X + 3 >= X + 3 = mark(s(X))
    
    proper(2nd(X)) = X >= X = 2nd(proper(X))
    
    proper(cons(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = 2X + 6 >= 2X + 6 = from(proper(X))
    
    proper(s(X)) = X + 3 >= X + 3 = s(proper(X))
    
    top(mark(X)) = 2X >= 2X = top(proper(X))
   problem:
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(2nd(X)) -> 2nd(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    2nd(mark(X)) -> mark(2nd(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    from(mark(X)) -> mark(from(X))
    s(mark(X)) -> mark(s(X))
    proper(2nd(X)) -> 2nd(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    proper(s(X)) -> s(proper(X))
    top(mark(X)) -> top(proper(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [from](x0) = 5x0 + 2,
     
     [top](x0) = 2x0 + 1,
     
     [2nd](x0) = 4x0 + 4,
     
     [mark](x0) = x0 + 1,
     
     [s](x0) = 2x0 + 1,
     
     [cons](x0, x1) = 6x0 + x1,
     
     [proper](x0) = x0,
     
     [active](x0) = 4x0
    orientation:
     active(from(X)) = 20X + 8 >= 16X + 8 = mark(cons(X,from(s(X))))
     
     active(2nd(X)) = 16X + 16 >= 16X + 4 = 2nd(active(X))
     
     active(cons(X1,X2)) = 24X1 + 4X2 >= 24X1 + X2 = cons(active(X1),X2)
     
     2nd(mark(X)) = 4X + 8 >= 4X + 5 = mark(2nd(X))
     
     cons(mark(X1),X2) = 6X1 + X2 + 6 >= 6X1 + X2 + 1 = mark(cons(X1,X2))
     
     from(mark(X)) = 5X + 7 >= 5X + 3 = mark(from(X))
     
     s(mark(X)) = 2X + 3 >= 2X + 2 = mark(s(X))
     
     proper(2nd(X)) = 4X + 4 >= 4X + 4 = 2nd(proper(X))
     
     proper(cons(X1,X2)) = 6X1 + X2 >= 6X1 + X2 = cons(proper(X1),proper(X2))
     
     proper(from(X)) = 5X + 2 >= 5X + 2 = from(proper(X))
     
     proper(s(X)) = 2X + 1 >= 2X + 1 = s(proper(X))
     
     top(mark(X)) = 2X + 3 >= 2X + 1 = top(proper(X))
    problem:
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [from](x0) = x0,
      
      [2nd](x0) = 2x0 + 2,
      
      [mark](x0) = x0,
      
      [s](x0) = 2x0,
      
      [cons](x0, x1) = 2x0 + 2x1,
      
      [proper](x0) = 4x0,
      
      [active](x0) = 6x0
     orientation:
      active(from(X)) = 6X >= 6X = mark(cons(X,from(s(X))))
      
      active(cons(X1,X2)) = 12X1 + 12X2 >= 12X1 + 2X2 = cons(active(X1),X2)
      
      proper(2nd(X)) = 8X + 8 >= 8X + 2 = 2nd(proper(X))
      
      proper(cons(X1,X2)) = 8X1 + 8X2 >= 8X1 + 8X2 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = 4X >= 4X = from(proper(X))
      
      proper(s(X)) = 8X >= 8X = s(proper(X))
     problem:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(from(X)) -> from(proper(X))
      proper(s(X)) -> s(proper(X))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [from](x0) = 6x0,
       
       [mark](x0) = 4x0,
       
       [s](x0) = x0,
       
       [cons](x0, x1) = x0 + x1 + 1,
       
       [proper](x0) = x0,
       
       [active](x0) = 5x0 + 6
      orientation:
       active(from(X)) = 30X + 6 >= 28X + 4 = mark(cons(X,from(s(X))))
       
       active(cons(X1,X2)) = 5X1 + 5X2 + 11 >= 5X1 + X2 + 7 = cons(active(X1),X2)
       
       proper(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(proper(X1),proper(X2))
       
       proper(from(X)) = 6X >= 6X = from(proper(X))
       
       proper(s(X)) = X >= X = s(proper(X))
      problem:
       proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
       proper(from(X)) -> from(proper(X))
       proper(s(X)) -> s(proper(X))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [from](x0) = x0,
        
        [s](x0) = 2x0 + 2,
        
        [cons](x0, x1) = x0 + x1 + 1,
        
        [proper](x0) = 2x0 + 1
       orientation:
        proper(cons(X1,X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = cons(proper(X1),proper(X2))
        
        proper(from(X)) = 2X + 1 >= 2X + 1 = from(proper(X))
        
        proper(s(X)) = 4X + 5 >= 4X + 4 = s(proper(X))
       problem:
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(from(X)) -> from(proper(X))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                      [1 0 0]     [0]
         [from](x0) = [0 0 1]x0 + [1]
                      [0 1 0]     [0],
         
                               [1 0 0]     [0]
         [cons](x0, x1) = x0 + [0 0 1]x1 + [1]
                               [0 1 0]     [0],
         
                        [1 1 1]  
         [proper](x0) = [0 1 0]x0
                        [0 0 1]  
        orientation:
                               [1 1 1]     [1 1 1]     [1]    [1 1 1]     [1 1 1]     [0]                              
         proper(cons(X1,X2)) = [0 1 0]X1 + [0 0 1]X2 + [1] >= [0 1 0]X1 + [0 0 1]X2 + [1] = cons(proper(X1),proper(X2))
                               [0 0 1]     [0 1 0]     [0]    [0 0 1]     [0 1 0]     [0]                              
         
                           [1 1 1]    [1]    [1 1 1]    [0]                  
         proper(from(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = from(proper(X))
                           [0 1 0]    [0]    [0 1 0]    [0]                  
        problem:
         
        Qed