/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:
 a__zeros() -> cons(0(),zeros())
 a__tail(cons(X,XS)) -> mark(XS)
 mark(zeros()) -> a__zeros()
 mark(tail(X)) -> a__tail(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 a__zeros() -> zeros()
 a__tail(X) -> tail(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 0 0]     [1]
   [tail](x0) = [0 1 0]x0 + [0]
                [0 0 0]     [0],
   
                [1 1 0]     [0]
   [mark](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0],
   
                   [1 0 0]     [1]
   [a__tail](x0) = [0 1 1]x0 + [0]
                   [0 0 0]     [0],
   
                    [1 1 0]     [1 1 0]     [0]
   [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                    [0 0 0]     [0 0 0]     [0],
   
             [1]
   [zeros] = [0]
             [0],
   
         [0]
   [0] = [0]
         [0],
   
                [1]
   [a__zeros] = [1]
                [0]
  orientation:
                [1]    [1]                    
   a__zeros() = [1] >= [1] = cons(0(),zeros())
                [0]    [0]                    
   
                         [1 1 0]    [1 1 0]     [1]    [1 1 0]     [0]           
   a__tail(cons(X,XS)) = [0 0 0]X + [0 0 0]XS + [1] >= [0 0 0]XS + [1] = mark(XS)
                         [0 0 0]    [0 0 0]     [0]    [0 0 0]     [0]           
   
                   [1]    [1]             
   mark(zeros()) = [1] >= [1] = a__zeros()
                   [0]    [0]             
   
                   [1 1 0]    [1]    [1 1 0]    [1]                   
   mark(tail(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__tail(mark(X))
                   [0 0 0]    [0]    [0 0 0]    [0]                   
   
                       [1 1 0]     [1 1 0]     [1]    [1 1 0]     [1 1 0]     [1]                    
   mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2)
                       [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]     [0]                    
   
               [0]    [0]      
   mark(0()) = [1] >= [0] = 0()
               [0]    [0]      
   
                [1]    [1]          
   a__zeros() = [1] >= [0] = zeros()
                [0]    [0]          
   
                [1 0 0]    [1]    [1 0 0]    [1]          
   a__tail(X) = [0 1 1]X + [0] >= [0 1 0]X + [0] = tail(X)
                [0 0 0]    [0]    [0 0 0]    [0]          
  problem:
   a__zeros() -> cons(0(),zeros())
   mark(zeros()) -> a__zeros()
   mark(tail(X)) -> a__tail(mark(X))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(0()) -> 0()
   a__zeros() -> zeros()
   a__tail(X) -> tail(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                      [0]
    [tail](x0) = x0 + [1]
                      [0],
    
                 [1 1 1]  
    [mark](x0) = [1 1 1]x0
                 [0 0 1]  ,
    
                         [1]
    [a__tail](x0) = x0 + [1]
                         [0],
    
                          [1 0 0]     [0]
    [cons](x0, x1) = x0 + [0 0 0]x1 + [1]
                          [0 0 0]     [0],
    
              [0]
    [zeros] = [0]
              [1],
    
          [0]
    [0] = [0]
          [0],
    
                 [1]
    [a__zeros] = [1]
                 [1]
   orientation:
                 [1]    [0]                    
    a__zeros() = [1] >= [1] = cons(0(),zeros())
                 [1]    [0]                    
    
                    [1]    [1]             
    mark(zeros()) = [1] >= [1] = a__zeros()
                    [1]    [1]             
    
                    [1 1 1]    [1]    [1 1 1]    [1]                   
    mark(tail(X)) = [1 1 1]X + [1] >= [1 1 1]X + [1] = a__tail(mark(X))
                    [0 0 1]    [0]    [0 0 1]    [0]                   
    
                        [1 1 1]     [1 0 0]     [1]    [1 1 1]     [1 0 0]     [0]                    
    mark(cons(X1,X2)) = [1 1 1]X1 + [1 0 0]X2 + [1] >= [1 1 1]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2)
                        [0 0 1]     [0 0 0]     [0]    [0 0 1]     [0 0 0]     [0]                    
    
                [0]    [0]      
    mark(0()) = [0] >= [0] = 0()
                [0]    [0]      
    
                 [1]    [0]          
    a__zeros() = [1] >= [0] = zeros()
                 [1]    [1]          
    
                     [1]        [0]          
    a__tail(X) = X + [1] >= X + [1] = tail(X)
                     [0]        [0]          
   problem:
    mark(zeros()) -> a__zeros()
    mark(tail(X)) -> a__tail(mark(X))
    mark(0()) -> 0()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 1 0]  
     [tail](x0) = [0 0 0]x0
                  [0 0 1]  ,
     
                  [1 1 0]  
     [mark](x0) = [0 1 1]x0
                  [0 0 1]  ,
     
                     [1 0 0]  
     [a__tail](x0) = [0 0 1]x0
                     [0 0 1]  ,
     
               [1]
     [zeros] = [0]
               [0],
     
           [0]
     [0] = [1]
           [0],
     
                  [0]
     [a__zeros] = [0]
                  [0]
    orientation:
                     [1]    [0]             
     mark(zeros()) = [0] >= [0] = a__zeros()
                     [0]    [0]             
     
                     [1 1 0]     [1 1 0]                    
     mark(tail(X)) = [0 0 1]X >= [0 0 1]X = a__tail(mark(X))
                     [0 0 1]     [0 0 1]                    
     
                 [1]    [0]      
     mark(0()) = [1] >= [1] = 0()
                 [0]    [0]      
    problem:
     mark(tail(X)) -> a__tail(mark(X))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                   [1 0 0]     [1]
      [tail](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [0],
      
                   [1 0 0]  
      [mark](x0) = [0 0 0]x0
                   [0 0 0]  ,
      
                      [1 0 0]  
      [a__tail](x0) = [0 0 0]x0
                      [0 0 0]  
     orientation:
                      [1 0 0]    [1]    [1 0 0]                    
      mark(tail(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__tail(mark(X))
                      [0 0 0]    [0]    [0 0 0]                    
     problem:
      
     Qed