/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 fst(0(),Z) -> nil()
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 from(X) -> cons(X,n__from(s(X)))
 add(0(),X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 len(nil()) -> 0()
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 from(X) -> n__from(X)
 add(X1,X2) -> n__add(X1,X2)
 len(X) -> n__len(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [n__len](x0) = x0,
   
   [len](x0) = 2x0,
   
   [n__add](x0, x1) = x0 + 4x1 + 3,
   
   [add](x0, x1) = 2x0 + 4x1 + 5,
   
   [n__from](x0) = x0 + 2,
   
   [from](x0) = 2x0 + 4,
   
   [n__fst](x0, x1) = 2x0 + 2x1,
   
   [activate](x0) = 2x0,
   
   [cons](x0, x1) = x0 + x1,
   
   [s](x0) = x0,
   
   [nil] = 0,
   
   [fst](x0, x1) = 4x0 + 4x1,
   
   [0] = 0
  orientation:
   fst(0(),Z) = 4Z >= 0 = nil()
   
   fst(s(X),cons(Y,Z)) = 4X + 4Y + 4Z >= 4X + Y + 4Z = cons(Y,n__fst(activate(X),activate(Z)))
   
   from(X) = 2X + 4 >= 2X + 2 = cons(X,n__from(s(X)))
   
   add(0(),X) = 4X + 5 >= X = X
   
   add(s(X),Y) = 2X + 4Y + 5 >= 2X + 4Y + 3 = s(n__add(activate(X),Y))
   
   len(nil()) = 0 >= 0 = 0()
   
   len(cons(X,Z)) = 2X + 2Z >= 2Z = s(n__len(activate(Z)))
   
   fst(X1,X2) = 4X1 + 4X2 >= 2X1 + 2X2 = n__fst(X1,X2)
   
   from(X) = 2X + 4 >= X + 2 = n__from(X)
   
   add(X1,X2) = 2X1 + 4X2 + 5 >= X1 + 4X2 + 3 = n__add(X1,X2)
   
   len(X) = 2X >= X = n__len(X)
   
   activate(n__fst(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = fst(X1,X2)
   
   activate(n__from(X)) = 2X + 4 >= 2X + 4 = from(X)
   
   activate(n__add(X1,X2)) = 2X1 + 8X2 + 6 >= 2X1 + 4X2 + 5 = add(X1,X2)
   
   activate(n__len(X)) = 2X >= 2X = len(X)
   
   activate(X) = 2X >= X = X
  problem:
   fst(0(),Z) -> nil()
   fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
   len(nil()) -> 0()
   len(cons(X,Z)) -> s(n__len(activate(Z)))
   fst(X1,X2) -> n__fst(X1,X2)
   len(X) -> n__len(X)
   activate(n__fst(X1,X2)) -> fst(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__len(X)) -> len(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [n__len](x0) = x0 + 1,
    
    [len](x0) = x0 + 1,
    
    [n__from](x0) = 5x0,
    
    [from](x0) = 4x0,
    
    [n__fst](x0, x1) = x0 + 4x1 + 3,
    
    [activate](x0) = x0,
    
    [cons](x0, x1) = x0 + 2x1 + 1,
    
    [s](x0) = 2x0,
    
    [nil] = 3,
    
    [fst](x0, x1) = x0 + 4x1 + 3,
    
    [0] = 4
   orientation:
    fst(0(),Z) = 4Z + 7 >= 3 = nil()
    
    fst(s(X),cons(Y,Z)) = 2X + 4Y + 8Z + 7 >= 2X + Y + 8Z + 7 = cons(Y,n__fst(activate(X),activate(Z)))
    
    len(nil()) = 4 >= 4 = 0()
    
    len(cons(X,Z)) = X + 2Z + 2 >= 2Z + 2 = s(n__len(activate(Z)))
    
    fst(X1,X2) = X1 + 4X2 + 3 >= X1 + 4X2 + 3 = n__fst(X1,X2)
    
    len(X) = X + 1 >= X + 1 = n__len(X)
    
    activate(n__fst(X1,X2)) = X1 + 4X2 + 3 >= X1 + 4X2 + 3 = fst(X1,X2)
    
    activate(n__from(X)) = 5X >= 4X = from(X)
    
    activate(n__len(X)) = X + 1 >= X + 1 = len(X)
    
    activate(X) = X >= X = X
   problem:
    fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
    len(nil()) -> 0()
    len(cons(X,Z)) -> s(n__len(activate(Z)))
    fst(X1,X2) -> n__fst(X1,X2)
    len(X) -> n__len(X)
    activate(n__fst(X1,X2)) -> fst(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__len(X)) -> len(X)
    activate(X) -> X
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [n__len](x0) = x0,
     
     [len](x0) = 2x0,
     
     [n__from](x0) = 4x0 + 6,
     
     [from](x0) = x0,
     
     [n__fst](x0, x1) = x0 + x1 + 4,
     
     [activate](x0) = 2x0,
     
     [cons](x0, x1) = 4x0 + x1 + 1,
     
     [s](x0) = x0 + 1,
     
     [nil] = 1,
     
     [fst](x0, x1) = 2x0 + 2x1 + 6,
     
     [0] = 0
    orientation:
     fst(s(X),cons(Y,Z)) = 2X + 8Y + 2Z + 10 >= 2X + 4Y + 2Z + 5 = cons(Y,n__fst(activate(X),activate(Z)))
     
     len(nil()) = 2 >= 0 = 0()
     
     len(cons(X,Z)) = 8X + 2Z + 2 >= 2Z + 1 = s(n__len(activate(Z)))
     
     fst(X1,X2) = 2X1 + 2X2 + 6 >= X1 + X2 + 4 = n__fst(X1,X2)
     
     len(X) = 2X >= X = n__len(X)
     
     activate(n__fst(X1,X2)) = 2X1 + 2X2 + 8 >= 2X1 + 2X2 + 6 = fst(X1,X2)
     
     activate(n__from(X)) = 8X + 12 >= X = from(X)
     
     activate(n__len(X)) = 2X >= 2X = len(X)
     
     activate(X) = 2X >= X = X
    problem:
     len(X) -> n__len(X)
     activate(n__len(X)) -> len(X)
     activate(X) -> X
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                     [1 0 0]  
      [n__len](x0) = [1 0 0]x0
                     [0 0 0]  ,
      
                  [1 0 0]     [1]
      [len](x0) = [1 0 0]x0 + [0]
                  [0 0 0]     [0],
      
                            [1]
      [activate](x0) = x0 + [0]
                            [0]
     orientation:
               [1 0 0]    [1]    [1 0 0]             
      len(X) = [1 0 0]X + [0] >= [1 0 0]X = n__len(X)
               [0 0 0]    [0]    [0 0 0]             
      
                            [1 0 0]    [1]    [1 0 0]    [1]         
      activate(n__len(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = len(X)
                            [0 0 0]    [0]    [0 0 0]    [0]         
      
                        [1]         
      activate(X) = X + [0] >= X = X
                        [0]         
     problem:
      activate(n__len(X)) -> len(X)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                      [1 0 0]  
       [n__len](x0) = [0 0 0]x0
                      [0 0 0]  ,
       
                   [1 0 0]  
       [len](x0) = [0 0 0]x0
                   [0 0 0]  ,
       
                        [1 0 0]     [1]
       [activate](x0) = [0 0 0]x0 + [0]
                        [0 0 0]     [0]
      orientation:
                             [1 0 0]    [1]    [1 0 0]          
       activate(n__len(X)) = [0 0 0]X + [0] >= [0 0 0]X = len(X)
                             [0 0 0]    [0]    [0 0 0]          
      problem:
       
      Qed