/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 active(zeros()) -> mark(cons(0(),zeros()))
 active(tail(cons(X,XS))) -> mark(XS)
 mark(zeros()) -> active(zeros())
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(0()) -> active(0())
 mark(tail(X)) -> active(tail(mark(X)))
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 tail(mark(X)) -> tail(X)
 tail(active(X)) -> tail(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [tail](x0) = x0 + 1,
   
   [mark](x0) = x0,
   
   [cons](x0, x1) = 4x0 + x1,
   
   [0] = 0,
   
   [active](x0) = x0,
   
   [zeros] = 0
  orientation:
   active(zeros()) = 0 >= 0 = mark(cons(0(),zeros()))
   
   active(tail(cons(X,XS))) = 4X + XS + 1 >= XS = mark(XS)
   
   mark(zeros()) = 0 >= 0 = active(zeros())
   
   mark(cons(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active(cons(mark(X1),X2))
   
   mark(0()) = 0 >= 0 = active(0())
   
   mark(tail(X)) = X + 1 >= X + 1 = active(tail(mark(X)))
   
   cons(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2)
   
   cons(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2)
   
   cons(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2)
   
   cons(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2)
   
   tail(mark(X)) = X + 1 >= X + 1 = tail(X)
   
   tail(active(X)) = X + 1 >= X + 1 = tail(X)
  problem:
   active(zeros()) -> mark(cons(0(),zeros()))
   mark(zeros()) -> active(zeros())
   mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
   mark(0()) -> active(0())
   mark(tail(X)) -> active(tail(mark(X)))
   cons(mark(X1),X2) -> cons(X1,X2)
   cons(X1,mark(X2)) -> cons(X1,X2)
   cons(active(X1),X2) -> cons(X1,X2)
   cons(X1,active(X2)) -> cons(X1,X2)
   tail(mark(X)) -> tail(X)
   tail(active(X)) -> tail(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 1]     [1]
    [tail](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
                 [1 0 1]  
    [mark](x0) = [1 1 0]x0
                 [0 0 0]  ,
    
                     [1 0 1]     [1 0 0]  
    [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 1 0]  ,
    
          [0]
    [0] = [0]
          [0],
    
                   [1 0 1]  
    [active](x0) = [0 1 0]x0
                   [0 0 0]  ,
    
              [0]
    [zeros] = [0]
              [1]
   orientation:
                      [1]    [0]                          
    active(zeros()) = [0] >= [0] = mark(cons(0(),zeros()))
                      [0]    [0]                          
    
                    [1]    [1]                  
    mark(zeros()) = [0] >= [0] = active(zeros())
                    [0]    [0]                  
    
                        [1 0 1]     [1 1 0]      [1 0 1]     [1 1 0]                              
    mark(cons(X1,X2)) = [1 1 1]X1 + [1 0 0]X2 >= [1 1 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2))
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                              
    
                [0]    [0]              
    mark(0()) = [0] >= [0] = active(0())
                [0]    [0]              
    
                    [1 0 1]    [1]    [1 0 1]    [1]                        
    mark(tail(X)) = [1 0 1]X + [1] >= [0 0 0]X + [0] = active(tail(mark(X)))
                    [0 0 0]    [0]    [0 0 0]    [0]                        
    
                        [1 0 1]     [1 0 0]      [1 0 1]     [1 0 0]                
    cons(mark(X1),X2) = [1 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(X1,X2)
                        [0 0 0]     [0 1 0]      [0 0 0]     [0 1 0]                
    
                        [1 0 1]     [1 0 1]      [1 0 1]     [1 0 0]                
    cons(X1,mark(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(X1,X2)
                        [0 0 0]     [1 1 0]      [0 0 0]     [0 1 0]                
    
                          [1 0 1]     [1 0 0]      [1 0 1]     [1 0 0]                
    cons(active(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(X1,X2)
                          [0 0 0]     [0 1 0]      [0 0 0]     [0 1 0]                
    
                          [1 0 1]     [1 0 1]      [1 0 1]     [1 0 0]                
    cons(X1,active(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(X1,X2)
                          [0 0 0]     [0 1 0]      [0 0 0]     [0 1 0]                
    
                    [1 0 1]    [1]    [1 0 1]    [1]          
    tail(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = tail(X)
                    [0 0 0]    [0]    [0 0 0]    [0]          
    
                      [1 0 1]    [1]    [1 0 1]    [1]          
    tail(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = tail(X)
                      [0 0 0]    [0]    [0 0 0]    [0]          
   problem:
    mark(zeros()) -> active(zeros())
    mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    mark(0()) -> active(0())
    mark(tail(X)) -> active(tail(mark(X)))
    cons(mark(X1),X2) -> cons(X1,X2)
    cons(X1,mark(X2)) -> cons(X1,X2)
    cons(active(X1),X2) -> cons(X1,X2)
    cons(X1,active(X2)) -> cons(X1,X2)
    tail(mark(X)) -> tail(X)
    tail(active(X)) -> tail(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [tail](x0) = x0 + 5,
     
     [mark](x0) = 2x0 + 3,
     
     [cons](x0, x1) = 3x0 + 2x1 + 6,
     
     [0] = 0,
     
     [active](x0) = x0,
     
     [zeros] = 0
    orientation:
     mark(zeros()) = 3 >= 0 = active(zeros())
     
     mark(cons(X1,X2)) = 6X1 + 4X2 + 15 >= 6X1 + 2X2 + 15 = active(cons(mark(X1),X2))
     
     mark(0()) = 3 >= 0 = active(0())
     
     mark(tail(X)) = 2X + 13 >= 2X + 8 = active(tail(mark(X)))
     
     cons(mark(X1),X2) = 6X1 + 2X2 + 15 >= 3X1 + 2X2 + 6 = cons(X1,X2)
     
     cons(X1,mark(X2)) = 3X1 + 4X2 + 12 >= 3X1 + 2X2 + 6 = cons(X1,X2)
     
     cons(active(X1),X2) = 3X1 + 2X2 + 6 >= 3X1 + 2X2 + 6 = cons(X1,X2)
     
     cons(X1,active(X2)) = 3X1 + 2X2 + 6 >= 3X1 + 2X2 + 6 = cons(X1,X2)
     
     tail(mark(X)) = 2X + 8 >= X + 5 = tail(X)
     
     tail(active(X)) = X + 5 >= X + 5 = tail(X)
    problem:
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     tail(active(X)) -> tail(X)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [tail](x0) = 6x0 + 4,
      
      [mark](x0) = 2x0 + 4,
      
      [cons](x0, x1) = x0 + 4x1 + 4,
      
      [active](x0) = x0 + 4
     orientation:
      mark(cons(X1,X2)) = 2X1 + 8X2 + 12 >= 2X1 + 4X2 + 12 = active(cons(mark(X1),X2))
      
      cons(active(X1),X2) = X1 + 4X2 + 8 >= X1 + 4X2 + 4 = cons(X1,X2)
      
      cons(X1,active(X2)) = X1 + 4X2 + 20 >= X1 + 4X2 + 4 = cons(X1,X2)
      
      tail(active(X)) = 6X + 28 >= 6X + 4 = tail(X)
     problem:
      mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                    [1 0 1]  
       [mark](x0) = [0 0 0]x0
                    [0 1 0]  ,
       
                        [1 0 0]     [1 0 0]     [0]
       [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                        [0 0 1]     [0 0 0]     [1],
       
                      [1 0 0]  
       [active](x0) = [0 0 0]x0
                      [0 0 0]  
      orientation:
                           [1 0 1]     [1 0 0]     [1]    [1 0 1]     [1 0 0]                              
       mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2))
                           [0 0 0]     [0 0 1]     [0]    [0 0 0]     [0 0 0]                              
      problem:
       
      Qed