/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:
 2nd(cons1(X,cons(Y,Z))) -> Y
 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                   [1 1]  
   [n__from](x0) = [0 0]x0,
   
             [1 0]  
   [s](x0) = [0 0]x0,
   
                [3 1]     [0]
   [from](x0) = [2 0]x0 + [3],
   
                    [3 3]     [0]
   [activate](x0) = [2 1]x0 + [3],
   
               [1 2]     [0]
   [2nd](x0) = [1 2]x0 + [1],
   
                     [1 1]     [2 0]     [2]
   [cons1](x0, x1) = [0 0]x0 + [0 0]x1 + [1],
   
                    [1 1]     [2 0]     [0]
   [cons](x0, x1) = [0 0]x0 + [2 3]x1 + [2]
  orientation:
                             [1 1]    [2 2]    [4 0]    [4]         
   2nd(cons1(X,cons(Y,Z))) = [1 1]X + [2 2]Y + [4 0]Z + [5] >= Y = Y
   
                     [1 1]    [6 6]     [4]    [1 1]    [6 6]     [4]                             
   2nd(cons(X,X1)) = [1 1]X + [6 6]X1 + [5] >= [1 1]X + [6 6]X1 + [5] = 2nd(cons1(X,activate(X1)))
   
             [3 1]    [0]    [3 1]    [0]                        
   from(X) = [2 0]X + [3] >= [2 0]X + [2] = cons(X,n__from(s(X)))
   
             [3 1]    [0]    [1 1]              
   from(X) = [2 0]X + [3] >= [0 0]X = n__from(X)
   
                          [3 3]    [0]    [3 1]    [0]          
   activate(n__from(X)) = [2 2]X + [3] >= [2 0]X + [3] = from(X)
   
                 [3 3]    [0]         
   activate(X) = [2 1]X + [3] >= X = X
  problem:
   2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   from(X) -> cons(X,n__from(s(X)))
   from(X) -> n__from(X)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                    [1 2]     [2]
    [n__from](x0) = [0 0]x0 + [0],
    
              [1 0]  
    [s](x0) = [0 0]x0,
    
                 [2 2]     [2]
    [from](x0) = [1 0]x0 + [3],
    
                     [2 0]  
    [activate](x0) = [2 2]x0,
    
                [2 2]  
    [2nd](x0) = [1 1]x0,
    
                      [1 0]     [1 0]  
    [cons1](x0, x1) = [0 0]x0 + [0 0]x1,
    
                     [1 1]     [1 0]     [0]
    [cons](x0, x1) = [0 0]x0 + [1 1]x1 + [1]
   orientation:
                      [2 2]    [4 2]     [2]    [2 0]    [4 0]                               
    2nd(cons(X,X1)) = [1 1]X + [2 1]X1 + [1] >= [1 0]X + [2 0]X1 = 2nd(cons1(X,activate(X1)))
    
              [2 2]    [2]    [2 1]    [2]                        
    from(X) = [1 0]X + [3] >= [1 0]X + [3] = cons(X,n__from(s(X)))
    
              [2 2]    [2]    [1 2]    [2]             
    from(X) = [1 0]X + [3] >= [0 0]X + [0] = n__from(X)
    
                           [2 4]    [4]    [2 2]    [2]          
    activate(n__from(X)) = [2 4]X + [4] >= [1 0]X + [3] = from(X)
    
                  [2 0]          
    activate(X) = [2 2]X >= X = X
   problem:
    from(X) -> cons(X,n__from(s(X)))
    from(X) -> n__from(X)
    activate(X) -> X
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [n__from](x0) = x0,
     
     [s](x0) = x0,
     
     [from](x0) = 5x0 + 5,
     
     [activate](x0) = x0 + 2,
     
     [cons](x0, x1) = x0 + 4x1
    orientation:
     from(X) = 5X + 5 >= 5X = cons(X,n__from(s(X)))
     
     from(X) = 5X + 5 >= X = n__from(X)
     
     activate(X) = X + 2 >= X = X
    problem:
     
    Qed