/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:
 int(0(),0()) -> .(0(),nil())
 int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
 int(s(x),0()) -> nil()
 int(s(x),s(y)) -> int_list(int(x,y))
 int_list(nil()) -> nil()
 int_list(.(x,y)) -> .(s(x),int_list(y))

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