/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:
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 from(X) -> cons(X,n__from(s(X)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> n__from(X)
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [n__from](x0) = x0 + 2,
   
   [from](x0) = 2x0 + 7,
   
   [n__first](x0, x1) = 4x0 + 2x1 + 2,
   
   [activate](x0) = 2x0 + 4,
   
   [cons](x0, x1) = x0 + x1 + 1,
   
   [s](x0) = x0 + 4,
   
   [nil] = 0,
   
   [first](x0, x1) = 4x0 + 4x1 + 3,
   
   [0] = 0
  orientation:
   first(0(),X) = 4X + 3 >= 0 = nil()
   
   first(s(X),cons(Y,Z)) = 4X + 4Y + 4Z + 23 >= 4X + Y + 4Z + 11 = cons(Y,n__first(X,activate(Z)))
   
   from(X) = 2X + 7 >= 2X + 7 = cons(X,n__from(s(X)))
   
   first(X1,X2) = 4X1 + 4X2 + 3 >= 4X1 + 2X2 + 2 = n__first(X1,X2)
   
   from(X) = 2X + 7 >= X + 2 = n__from(X)
   
   activate(n__first(X1,X2)) = 8X1 + 4X2 + 8 >= 4X1 + 4X2 + 3 = first(X1,X2)
   
   activate(n__from(X)) = 2X + 8 >= 2X + 7 = from(X)
   
   activate(X) = 2X + 4 >= X = X
  problem:
   from(X) -> cons(X,n__from(s(X)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [n__from](x0) = x0 + 1,
    
    [from](x0) = 5x0 + 5,
    
    [cons](x0, x1) = x0 + 4x1,
    
    [s](x0) = x0
   orientation:
    from(X) = 5X + 5 >= 5X + 4 = cons(X,n__from(s(X)))
   problem:
    
   Qed