/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:
 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:
                [3 1]     [1]
   [from](x0) = [3 1]x0 + [3],
   
                     [1 1]     [1 0]  
   [cons1](x0, x1) = [0 0]x0 + [0 0]x1,
   
                    [2 1]  
   [activate](x0) = [1 2]x0,
   
             [1 0]     [0]
   [s](x0) = [2 1]x0 + [1],
   
                    [1 1]     [2 0]  
   [cons](x0, x1) = [0 0]x0 + [0 1]x1,
   
                   [1 0]     [0]
   [n__from](x0) = [1 1]x0 + [2],
   
               [2 2]     [2]
   [2nd](x0) = [2 2]x0 + [0]
  orientation:
                             [2 2]    [2 2]    [4 0]    [2]         
   2nd(cons1(X,cons(Y,Z))) = [2 2]X + [2 2]Y + [4 0]Z + [0] >= Y = Y
   
                     [2 2]    [4 2]     [2]    [2 2]    [4 2]     [2]                             
   2nd(cons(X,X1)) = [2 2]X + [4 2]X1 + [0] >= [2 2]X + [4 2]X1 + [0] = 2nd(cons1(X,activate(X1)))
   
             [3 1]    [1]    [3 1]    [0]                        
   from(X) = [3 1]X + [3] >= [3 1]X + [3] = cons(X,n__from(s(X)))
   
             [3 1]    [1]    [1 0]    [0]             
   from(X) = [3 1]X + [3] >= [1 1]X + [2] = n__from(X)
   
                          [3 1]    [2]    [3 1]    [1]          
   activate(n__from(X)) = [3 2]X + [4] >= [3 1]X + [3] = from(X)
   
                 [2 1]          
   activate(X) = [1 2]X >= X = X
  problem:
   2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   activate(X) -> X
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [cons1](x0, x1) = 2x0 + 2x1 + 4,
    
    [activate](x0) = x0 + 1,
    
    [cons](x0, x1) = 4x0 + 7x1 + 6,
    
    [2nd](x0) = 3x0
   orientation:
    2nd(cons(X,X1)) = 12X + 21X1 + 18 >= 6X + 6X1 + 18 = 2nd(cons1(X,activate(X1)))
    
    activate(X) = X + 1 >= X = X
   problem:
    2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                       [1 0 0]     [1 0 0]  
     [cons1](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                       [0 0 0]     [0 0 0]  ,
     
                      [1 0 0]  
     [activate](x0) = [0 0 0]x0
                      [0 0 0]  ,
     
                      [1 0 0]     [1 0 0]     [0]
     [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                      [0 0 0]     [0 0 0]     [1],
     
                 [1 0 1]  
     [2nd](x0) = [0 0 0]x0
                 [0 0 0]  
    orientation:
                       [1 0 0]    [1 0 0]     [1]    [1 0 0]    [1 0 0]                               
     2nd(cons(X,X1)) = [0 0 0]X + [0 0 0]X1 + [0] >= [0 0 0]X + [0 0 0]X1 = 2nd(cons1(X,activate(X1)))
                       [0 0 0]    [0 0 0]     [0]    [0 0 0]    [0 0 0]                               
    problem:
     
    Qed