/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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:
   [top](x0) = 2x0,
   
   [ok](x0) = 4x0 + 1,
   
   [proper](x0) = x0,
   
   [s](x0) = x0,
   
   [from](x0) = 4x0 + 1,
   
   [mark](x0) = x0,
   
   [active](x0) = 4x0,
   
   [2nd](x0) = x0,
   
   [cons](x0, x1) = 6x0 + x1 + 2
  orientation:
   active(2nd(cons(X,cons(Y,Z)))) = 24X + 24Y + 4Z + 16 >= Y = mark(Y)
   
   active(from(X)) = 16X + 4 >= 10X + 3 = mark(cons(X,from(s(X))))
   
   active(2nd(X)) = 4X >= 4X = 2nd(active(X))
   
   active(cons(X1,X2)) = 24X1 + 4X2 + 8 >= 24X1 + X2 + 2 = cons(active(X1),X2)
   
   active(from(X)) = 16X + 4 >= 16X + 1 = from(active(X))
   
   active(s(X)) = 4X >= 4X = s(active(X))
   
   2nd(mark(X)) = X >= X = mark(2nd(X))
   
   cons(mark(X1),X2) = 6X1 + X2 + 2 >= 6X1 + X2 + 2 = mark(cons(X1,X2))
   
   from(mark(X)) = 4X + 1 >= 4X + 1 = mark(from(X))
   
   s(mark(X)) = X >= X = mark(s(X))
   
   proper(2nd(X)) = X >= X = 2nd(proper(X))
   
   proper(cons(X1,X2)) = 6X1 + X2 + 2 >= 6X1 + X2 + 2 = cons(proper(X1),proper(X2))
   
   proper(from(X)) = 4X + 1 >= 4X + 1 = from(proper(X))
   
   proper(s(X)) = X >= X = s(proper(X))
   
   2nd(ok(X)) = 4X + 1 >= 4X + 1 = ok(2nd(X))
   
   cons(ok(X1),ok(X2)) = 24X1 + 4X2 + 9 >= 24X1 + 4X2 + 9 = ok(cons(X1,X2))
   
   from(ok(X)) = 16X + 5 >= 16X + 5 = ok(from(X))
   
   s(ok(X)) = 4X + 1 >= 4X + 1 = ok(s(X))
   
   top(mark(X)) = 2X >= 2X = top(proper(X))
   
   top(ok(X)) = 8X + 2 >= 8X = top(active(X))
  problem:
   active(2nd(X)) -> 2nd(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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = x0 + 3,
    
    [ok](x0) = x0,
    
    [proper](x0) = x0,
    
    [s](x0) = x0 + 4,
    
    [from](x0) = 4x0,
    
    [mark](x0) = x0 + 5,
    
    [active](x0) = x0,
    
    [2nd](x0) = x0,
    
    [cons](x0, x1) = 2x0 + x1
   orientation:
    active(2nd(X)) = X >= X = 2nd(active(X))
    
    active(s(X)) = X + 4 >= X + 4 = s(active(X))
    
    2nd(mark(X)) = X + 5 >= X + 5 = mark(2nd(X))
    
    cons(mark(X1),X2) = 2X1 + X2 + 10 >= 2X1 + X2 + 5 = mark(cons(X1,X2))
    
    from(mark(X)) = 4X + 20 >= 4X + 5 = mark(from(X))
    
    s(mark(X)) = X + 9 >= X + 9 = mark(s(X))
    
    proper(2nd(X)) = X >= X = 2nd(proper(X))
    
    proper(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = 4X >= 4X = from(proper(X))
    
    proper(s(X)) = X + 4 >= X + 4 = s(proper(X))
    
    2nd(ok(X)) = X >= X = ok(2nd(X))
    
    cons(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(cons(X1,X2))
    
    from(ok(X)) = 4X >= 4X = ok(from(X))
    
    s(ok(X)) = X + 4 >= X + 4 = ok(s(X))
    
    top(mark(X)) = X + 8 >= X + 3 = top(proper(X))
   problem:
    active(2nd(X)) -> 2nd(active(X))
    active(s(X)) -> s(active(X))
    2nd(mark(X)) -> mark(2nd(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))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [ok](x0) = 4x0 + 4,
     
     [proper](x0) = 4x0,
     
     [s](x0) = 4x0 + 4,
     
     [from](x0) = 4x0 + 4,
     
     [mark](x0) = 2x0 + 4,
     
     [active](x0) = 4x0 + 1,
     
     [2nd](x0) = 3x0 + 2,
     
     [cons](x0, x1) = x0 + x1 + 1
    orientation:
     active(2nd(X)) = 12X + 9 >= 12X + 5 = 2nd(active(X))
     
     active(s(X)) = 16X + 17 >= 16X + 8 = s(active(X))
     
     2nd(mark(X)) = 6X + 14 >= 6X + 8 = mark(2nd(X))
     
     s(mark(X)) = 8X + 20 >= 8X + 12 = mark(s(X))
     
     proper(2nd(X)) = 12X + 8 >= 12X + 2 = 2nd(proper(X))
     
     proper(cons(X1,X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 1 = cons(proper(X1),proper(X2))
     
     proper(from(X)) = 16X + 16 >= 16X + 4 = from(proper(X))
     
     proper(s(X)) = 16X + 16 >= 16X + 4 = s(proper(X))
     
     2nd(ok(X)) = 12X + 14 >= 12X + 12 = ok(2nd(X))
     
     cons(ok(X1),ok(X2)) = 4X1 + 4X2 + 9 >= 4X1 + 4X2 + 8 = ok(cons(X1,X2))
     
     from(ok(X)) = 16X + 20 >= 16X + 20 = ok(from(X))
     
     s(ok(X)) = 16X + 20 >= 16X + 20 = ok(s(X))
    problem:
     from(ok(X)) -> ok(from(X))
     s(ok(X)) -> ok(s(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [ok](x0) = x0 + 7,
      
      [s](x0) = 4x0 + 1,
      
      [from](x0) = x0
     orientation:
      from(ok(X)) = X + 7 >= X + 7 = ok(from(X))
      
      s(ok(X)) = 4X + 29 >= 4X + 8 = ok(s(X))
     problem:
      from(ok(X)) -> ok(from(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                  [1 0 0]     [0]
       [ok](x0) = [0 0 0]x0 + [0]
                  [0 0 1]     [1],
       
                    [1 0 1]  
       [from](x0) = [0 0 0]x0
                    [0 0 1]  
      orientation:
                     [1 0 1]    [1]    [1 0 1]    [0]              
       from(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(from(X))
                     [0 0 1]    [1]    [0 0 1]    [1]              
      problem:
       
      Qed