/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:
 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:
   [cons](x0, x1) = x0 + 2x1 + 1,
   
   [n__from](x0) = x0,
   
   [first](x0, x1) = 7x0 + 6x1 + 5,
   
   [s](x0) = x0 + 2,
   
   [activate](x0) = 3x0 + 5,
   
   [0] = 0,
   
   [from](x0) = 3x0 + 5,
   
   [n__first](x0, x1) = 3x0 + 2x1 + 2,
   
   [nil] = 0
  orientation:
   first(0(),X) = 6X + 5 >= 0 = nil()
   
   first(s(X),cons(Y,Z)) = 7X + 6Y + 12Z + 25 >= 6X + Y + 12Z + 25 = cons(Y,n__first(X,activate(Z)))
   
   from(X) = 3X + 5 >= 3X + 5 = cons(X,n__from(s(X)))
   
   first(X1,X2) = 7X1 + 6X2 + 5 >= 3X1 + 2X2 + 2 = n__first(X1,X2)
   
   from(X) = 3X + 5 >= X = n__from(X)
   
   activate(n__first(X1,X2)) = 9X1 + 6X2 + 11 >= 7X1 + 6X2 + 5 = first(X1,X2)
   
   activate(n__from(X)) = 3X + 5 >= 3X + 5 = from(X)
   
   activate(X) = 3X + 5 >= X = X
  problem:
   first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
   from(X) -> cons(X,n__from(s(X)))
   activate(n__from(X)) -> from(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [cons](x0, x1) = x0 + x1 + 4,
    
    [n__from](x0) = x0 + 3,
    
    [first](x0, x1) = 2x0 + 7x1 + 2,
    
    [s](x0) = 4x0,
    
    [activate](x0) = 6x0 + 1,
    
    [from](x0) = 5x0 + 7,
    
    [n__first](x0, x1) = 4x0 + x1
   orientation:
    first(s(X),cons(Y,Z)) = 8X + 7Y + 7Z + 30 >= 4X + Y + 6Z + 5 = cons(Y,n__first(X,activate(Z)))
    
    from(X) = 5X + 7 >= 5X + 7 = cons(X,n__from(s(X)))
    
    activate(n__from(X)) = 6X + 19 >= 5X + 7 = from(X)
   problem:
    from(X) -> cons(X,n__from(s(X)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [cons](x0, x1) = 2x0 + 4x1,
     
     [n__from](x0) = x0,
     
     [s](x0) = x0,
     
     [from](x0) = 6x0 + 1
    orientation:
     from(X) = 6X + 1 >= 6X = cons(X,n__from(s(X)))
    problem:
     
    Qed