10.37/3.00	YES
10.37/3.00	
10.37/3.00	Problem:
10.37/3.00	 strict:
10.37/3.00	  not(true()) -> false()
10.37/3.00	  not(false()) -> true()
10.37/3.00	  evenodd(x,0()) -> not(evenodd(x,s(0())))
10.37/3.00	  evenodd(0(),s(0())) -> false()
10.37/3.00	  evenodd(s(x),s(0())) -> evenodd(x,0())
10.37/3.00	 weak:
10.37/3.00	  rand(x) -> x
10.37/3.00	  rand(x) -> rand(s(x))
10.37/3.00	
10.37/3.00	Proof:
10.37/3.00	 Matrix Interpretation Processor: dim=2
10.37/3.00	  
10.37/3.00	  interpretation:
10.37/3.00	                [2 2]     [2]
10.37/3.00	   [rand](x0) = [1 1]x0 + [0],
10.37/3.00	   
10.37/3.00	             [1 1]  
10.37/3.00	   [s](x0) = [0 0]x0,
10.37/3.00	   
10.37/3.00	                       [2 1]     [1 1]     [0]
10.37/3.00	   [evenodd](x0, x1) = [2 1]x0 + [0 0]x1 + [1],
10.37/3.00	   
10.37/3.00	         [0]
10.37/3.00	   [0] = [1],
10.37/3.00	   
10.37/3.00	             [0]
10.37/3.00	   [false] = [0],
10.37/3.00	   
10.37/3.00	               [1 0]     [0]
10.37/3.00	   [not](x0) = [0 0]x0 + [1],
10.37/3.00	   
10.37/3.00	            [0]
10.37/3.00	   [true] = [0]
10.37/3.00	  orientation:
10.37/3.00	                 [0]    [0]          
10.37/3.00	   not(true()) = [1] >= [0] = false()
10.37/3.00	   
10.37/3.00	                  [0]    [0]         
10.37/3.00	   not(false()) = [1] >= [0] = true()
10.37/3.00	   
10.37/3.00	                    [2 1]    [1]    [2 1]    [1]                         
10.37/3.00	   evenodd(x,0()) = [2 1]x + [1] >= [0 0]x + [1] = not(evenodd(x,s(0())))
10.37/3.00	   
10.37/3.00	                         [2]    [0]          
10.37/3.00	   evenodd(0(),s(0())) = [2] >= [0] = false()
10.37/3.00	   
10.37/3.00	                          [2 2]    [1]    [2 1]    [1]                 
10.37/3.00	   evenodd(s(x),s(0())) = [2 2]x + [1] >= [2 1]x + [1] = evenodd(x,0())
10.37/3.00	   
10.37/3.00	             [2 2]    [2]         
10.37/3.00	   rand(x) = [1 1]x + [0] >= x = x
10.37/3.00	   
10.37/3.00	             [2 2]    [2]    [2 2]    [2]             
10.37/3.00	   rand(x) = [1 1]x + [0] >= [1 1]x + [0] = rand(s(x))
10.37/3.00	  problem:
10.37/3.00	   strict:
10.37/3.00	    not(true()) -> false()
10.37/3.00	    not(false()) -> true()
10.37/3.00	    evenodd(x,0()) -> not(evenodd(x,s(0())))
10.37/3.00	    evenodd(s(x),s(0())) -> evenodd(x,0())
10.37/3.00	   weak:
10.37/3.00	    rand(x) -> rand(s(x))
10.37/3.00	  Matrix Interpretation Processor: dim=2
10.37/3.00	   
10.37/3.00	   interpretation:
10.37/3.00	                 [1 0]     [0]
10.37/3.00	    [rand](x0) = [0 0]x0 + [2],
10.37/3.00	    
10.37/3.00	                
10.37/3.00	    [s](x0) = x0,
10.37/3.00	    
10.37/3.00	                        [1 0]     [2 2]  
10.37/3.00	    [evenodd](x0, x1) = [0 0]x0 + [0 0]x1,
10.37/3.00	    
10.37/3.00	          [0]
10.37/3.00	    [0] = [1],
10.37/3.00	    
10.37/3.00	              [1]
10.37/3.00	    [false] = [1],
10.37/3.00	    
10.37/3.00	                [1 2]  
10.37/3.00	    [not](x0) = [0 2]x0,
10.37/3.00	    
10.37/3.00	             [0]
10.37/3.00	    [true] = [1]
10.37/3.00	   orientation:
10.37/3.00	                  [2]    [1]          
10.37/3.00	    not(true()) = [2] >= [1] = false()
10.37/3.00	    
10.37/3.00	                   [3]    [0]         
10.37/3.00	    not(false()) = [2] >= [1] = true()
10.37/3.00	    
10.37/3.00	                     [1 0]    [2]    [1 0]    [2]                         
10.37/3.00	    evenodd(x,0()) = [0 0]x + [0] >= [0 0]x + [0] = not(evenodd(x,s(0())))
10.37/3.00	    
10.37/3.00	                           [1 0]    [2]    [1 0]    [2]                 
10.37/3.00	    evenodd(s(x),s(0())) = [0 0]x + [0] >= [0 0]x + [0] = evenodd(x,0())
10.37/3.00	    
10.37/3.00	              [1 0]    [0]    [1 0]    [0]             
10.37/3.00	    rand(x) = [0 0]x + [2] >= [0 0]x + [2] = rand(s(x))
10.37/3.00	   problem:
10.37/3.00	    strict:
10.37/3.00	     evenodd(x,0()) -> not(evenodd(x,s(0())))
10.37/3.00	     evenodd(s(x),s(0())) -> evenodd(x,0())
10.37/3.00	    weak:
10.37/3.00	     rand(x) -> rand(s(x))
10.37/3.00	   Matrix Interpretation Processor: dim=2
10.37/3.00	    
10.37/3.00	    interpretation:
10.37/3.00	                  [2 0]  
10.37/3.00	     [rand](x0) = [0 0]x0,
10.37/3.00	     
10.37/3.00	                    [0]
10.37/3.00	     [s](x0) = x0 + [1],
10.37/3.00	     
10.37/3.00	                         [2 2]     [2 0]  
10.37/3.00	     [evenodd](x0, x1) = [0 0]x0 + [0 1]x1,
10.37/3.00	     
10.37/3.00	           [0]
10.37/3.00	     [0] = [0],
10.37/3.00	     
10.37/3.00	                 [1 0]  
10.37/3.00	     [not](x0) = [0 0]x0
10.37/3.00	    orientation:
10.37/3.00	                      [2 2]     [2 2]                          
10.37/3.00	     evenodd(x,0()) = [0 0]x >= [0 0]x = not(evenodd(x,s(0())))
10.37/3.00	     
10.37/3.00	                            [2 2]    [2]    [2 2]                  
10.37/3.00	     evenodd(s(x),s(0())) = [0 0]x + [1] >= [0 0]x = evenodd(x,0())
10.37/3.00	     
10.37/3.00	               [2 0]     [2 0]              
10.37/3.00	     rand(x) = [0 0]x >= [0 0]x = rand(s(x))
10.37/3.00	    problem:
10.37/3.00	     strict:
10.37/3.00	      evenodd(x,0()) -> not(evenodd(x,s(0())))
10.37/3.00	     weak:
10.37/3.00	      rand(x) -> rand(s(x))
10.37/3.00	    Matrix Interpretation Processor: dim=2
10.37/3.00	     
10.37/3.00	     interpretation:
10.37/3.00	                   [1 0]     [2]
10.37/3.00	      [rand](x0) = [1 2]x0 + [1],
10.37/3.00	      
10.37/3.00	                [1 0]  
10.37/3.00	      [s](x0) = [0 0]x0,
10.37/3.00	      
10.37/3.00	                          [1 2]     [2 1]     [2]
10.37/3.00	      [evenodd](x0, x1) = [2 2]x0 + [0 0]x1 + [1],
10.37/3.00	      
10.37/3.00	            [0]
10.37/3.00	      [0] = [1],
10.37/3.00	      
10.37/3.00	                  [1 0]     [0]
10.37/3.00	      [not](x0) = [0 0]x0 + [1]
10.37/3.00	     orientation:
10.37/3.00	                       [1 2]    [3]    [1 2]    [2]                         
10.37/3.00	      evenodd(x,0()) = [2 2]x + [1] >= [0 0]x + [1] = not(evenodd(x,s(0())))
10.37/3.00	      
10.37/3.00	                [1 0]    [2]    [1 0]    [2]             
10.37/3.00	      rand(x) = [1 2]x + [1] >= [1 0]x + [1] = rand(s(x))
10.37/3.00	     problem:
10.37/3.00	      strict:
10.37/3.00	       
10.37/3.00	      weak:
10.37/3.00	       rand(x) -> rand(s(x))
10.37/3.00	     Qed
10.60/3.01	EOF