/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:
 intlist(nil()) -> nil()
 int(s(x),0()) -> nil()
 int(x,x) -> cons(x,nil())
 intlist(cons(x,y)) -> cons(s(x),intlist(y))
 int(s(x),s(y)) -> intlist(int(x,y))
 int(0(),s(y)) -> cons(0(),int(s(0()),s(y)))
 intlist(cons(x,nil())) -> cons(s(x),nil())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [cons](x0, x1) = 2x0 + x1,
   
   [int](x0, x1) = x0 + 4x1 + 2,
   
   [0] = 0,
   
   [s](x0) = x0,
   
   [intlist](x0) = x0,
   
   [nil] = 0
  orientation:
   intlist(nil()) = 0 >= 0 = nil()
   
   int(s(x),0()) = x + 2 >= 0 = nil()
   
   int(x,x) = 5x + 2 >= 2x = cons(x,nil())
   
   intlist(cons(x,y)) = 2x + y >= 2x + y = cons(s(x),intlist(y))
   
   int(s(x),s(y)) = x + 4y + 2 >= x + 4y + 2 = intlist(int(x,y))
   
   int(0(),s(y)) = 4y + 2 >= 4y + 2 = cons(0(),int(s(0()),s(y)))
   
   intlist(cons(x,nil())) = 2x >= 2x = cons(s(x),nil())
  problem:
   intlist(nil()) -> nil()
   intlist(cons(x,y)) -> cons(s(x),intlist(y))
   int(s(x),s(y)) -> intlist(int(x,y))
   int(0(),s(y)) -> cons(0(),int(s(0()),s(y)))
   intlist(cons(x,nil())) -> cons(s(x),nil())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]     [1 0 0]  
    [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 1 1]  ,
    
                    [1 0 0]     [1 1 1]     [0]
    [int](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [1],
    
          [0]
    [0] = [0]
          [0],
    
              [1 0 0]     [0]
    [s](x0) = [0 1 1]x0 + [0]
              [0 0 0]     [1],
    
                    [1 0 1]  
    [intlist](x0) = [0 0 0]x0
                    [0 0 1]  ,
    
            [0]
    [nil] = [0]
            [1]
   orientation:
                     [1]    [0]        
    intlist(nil()) = [0] >= [0] = nil()
                     [1]    [1]        
    
                         [1 0 0]    [1 1 1]     [1 0 0]    [1 0 1]                         
    intlist(cons(x,y)) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = cons(s(x),intlist(y))
                         [0 0 0]    [0 1 1]     [0 0 0]    [0 0 1]                         
    
                     [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [1]                    
    int(s(x),s(y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = intlist(int(x,y))
                     [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]                    
    
                    [1 1 1]    [1]    [1 1 1]    [1]                             
    int(0(),s(y)) = [0 0 0]y + [0] >= [0 0 0]y + [0] = cons(0(),int(s(0()),s(y)))
                    [0 0 0]    [1]    [0 0 0]    [1]                             
    
                             [1 0 0]    [1]    [1 0 0]    [0]                   
    intlist(cons(x,nil())) = [0 0 0]x + [0] >= [0 0 0]x + [0] = cons(s(x),nil())
                             [0 0 0]    [1]    [0 0 0]    [1]                   
   problem:
    intlist(cons(x,y)) -> cons(s(x),intlist(y))
    int(s(x),s(y)) -> intlist(int(x,y))
    int(0(),s(y)) -> cons(0(),int(s(0()),s(y)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                      [1 0 0]     [1 0 0]  
     [cons](x0, x1) = [0 0 0]x0 + [1 0 0]x1
                      [0 0 0]     [0 0 0]  ,
     
                     [1 0 1]     [1 1 1]     [0]
     [int](x0, x1) = [0 0 0]x0 + [1 0 1]x1 + [1]
                     [1 0 0]     [0 0 0]     [1],
     
           [0]
     [0] = [0]
           [0],
     
               [1 0 0]     [0]
     [s](x0) = [0 0 0]x0 + [1]
               [0 1 1]     [0],
     
                       
     [intlist](x0) = x0
                       
    orientation:
                          [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]                         
     intlist(cons(x,y)) = [0 0 0]x + [1 0 0]y >= [0 0 0]x + [1 0 0]y = cons(s(x),intlist(y))
                          [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                         
     
                      [1 1 1]    [1 1 1]    [1]    [1 0 1]    [1 1 1]    [0]                    
     int(s(x),s(y)) = [0 0 0]x + [1 1 1]y + [1] >= [0 0 0]x + [1 0 1]y + [1] = intlist(int(x,y))
                      [1 0 0]    [0 0 0]    [1]    [1 0 0]    [0 0 0]    [1]                    
     
                     [1 1 1]    [1]    [1 1 1]    [1]                             
     int(0(),s(y)) = [1 1 1]y + [1] >= [1 1 1]y + [1] = cons(0(),int(s(0()),s(y)))
                     [0 0 0]    [1]    [0 0 0]    [0]                             
    problem:
     intlist(cons(x,y)) -> cons(s(x),intlist(y))
     int(0(),s(y)) -> cons(0(),int(s(0()),s(y)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                       [1 0 0]     [1 0 0]  
      [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                       [0 0 0]     [0 0 1]  ,
      
                      [1 1 0]     [1 0 1]  
      [int](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                      [0 0 0]     [0 1 0]  ,
      
            [0]
      [0] = [1]
            [1],
      
                [1 0 0]  
      [s](x0) = [1 0 0]x0
                [0 0 1]  ,
      
                      [1 0 0]     [1]
      [intlist](x0) = [0 0 0]x0 + [0]
                      [0 0 1]     [0]
     orientation:
                           [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]                        
      intlist(cons(x,y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = cons(s(x),intlist(y))
                           [0 0 0]    [0 0 1]    [0]    [0 0 0]    [0 0 1]    [0]                        
      
                      [1 0 1]    [1]    [1 0 1]                              
      int(0(),s(y)) = [0 0 0]y + [0] >= [0 0 0]y = cons(0(),int(s(0()),s(y)))
                      [1 0 0]    [0]    [1 0 0]                              
     problem:
      intlist(cons(x,y)) -> cons(s(x),intlist(y))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                        [1 0 0]     [1 0 0]     [0]
       [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                        [0 0 0]     [0 1 1]     [0],
       
                 [1 0 0]  
       [s](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
                       [1 1 1]     [0]
       [intlist](x0) = [0 0 0]x0 + [1]
                       [0 1 1]     [0]
      orientation:
                            [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [0]                        
       intlist(cons(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = cons(s(x),intlist(y))
                            [0 0 0]    [0 1 1]    [1]    [0 0 0]    [0 1 1]    [1]                        
      problem:
       
      Qed