16.38/4.48	YES
16.38/4.49	
16.38/4.49	Problem:
16.38/4.49	 strict:
16.38/4.49	  half(0()) -> 0()
16.38/4.49	  half(s(s(x))) -> s(half(x))
16.38/4.49	  log(s(0())) -> 0()
16.38/4.49	  log(s(s(x))) -> s(log(s(half(x))))
16.38/4.49	 weak:
16.38/4.49	  rand(x) -> x
16.38/4.49	  rand(x) -> rand(s(x))
16.38/4.49	
16.38/4.49	Proof:
16.38/4.49	 Arctic Interpretation Processor:
16.38/4.49	  dimension: 1
16.38/4.49	  interpretation:
16.38/4.49	   [rand](x0) = 2x0,
16.38/4.49	   
16.38/4.49	   [log](x0) = x0,
16.38/4.49	   
16.38/4.49	   [s](x0) = x0,
16.38/4.49	   
16.38/4.49	   [half](x0) = x0,
16.38/4.49	   
16.38/4.49	   [0] = 15
16.38/4.49	  orientation:
16.38/4.49	   half(0()) = 15 >= 15 = 0()
16.38/4.49	   
16.38/4.49	   half(s(s(x))) = x >= x = s(half(x))
16.38/4.49	   
16.38/4.49	   log(s(0())) = 15 >= 15 = 0()
16.38/4.49	   
16.38/4.49	   log(s(s(x))) = x >= x = s(log(s(half(x))))
16.38/4.49	   
16.38/4.49	   rand(x) = 2x >= x = x
16.38/4.49	   
16.38/4.49	   rand(x) = 2x >= 2x = rand(s(x))
16.38/4.49	  problem:
16.38/4.49	   strict:
16.38/4.49	    half(0()) -> 0()
16.38/4.49	    half(s(s(x))) -> s(half(x))
16.38/4.49	    log(s(0())) -> 0()
16.38/4.49	    log(s(s(x))) -> s(log(s(half(x))))
16.38/4.49	   weak:
16.38/4.49	    rand(x) -> rand(s(x))
16.38/4.49	  Arctic Interpretation Processor:
16.38/4.49	   dimension: 1
16.38/4.49	   interpretation:
16.38/4.49	    [rand](x0) = x0,
16.38/4.49	    
16.38/4.49	    [log](x0) = 4x0,
16.38/4.49	    
16.38/4.49	    [s](x0) = x0,
16.38/4.49	    
16.38/4.49	    [half](x0) = x0,
16.38/4.49	    
16.38/4.49	    [0] = 4
16.38/4.49	   orientation:
16.38/4.49	    half(0()) = 4 >= 4 = 0()
16.38/4.49	    
16.38/4.49	    half(s(s(x))) = x >= x = s(half(x))
16.38/4.49	    
16.38/4.49	    log(s(0())) = 8 >= 4 = 0()
16.38/4.49	    
16.38/4.49	    log(s(s(x))) = 4x >= 4x = s(log(s(half(x))))
16.38/4.49	    
16.38/4.49	    rand(x) = x >= x = rand(s(x))
16.38/4.49	   problem:
16.38/4.49	    strict:
16.38/4.49	     half(0()) -> 0()
16.38/4.49	     half(s(s(x))) -> s(half(x))
16.38/4.49	     log(s(s(x))) -> s(log(s(half(x))))
16.38/4.49	    weak:
16.38/4.49	     rand(x) -> rand(s(x))
16.38/4.49	   Matrix Interpretation Processor: dim=2
16.38/4.49	    
16.38/4.49	    interpretation:
16.38/4.49	                  [2 0]  
16.38/4.49	     [rand](x0) = [2 0]x0,
16.38/4.49	     
16.38/4.49	                 [2 1]     [0]
16.38/4.49	     [log](x0) = [1 1]x0 + [1],
16.38/4.49	     
16.38/4.49	                    [0]
16.38/4.49	     [s](x0) = x0 + [1],
16.38/4.49	     
16.38/4.49	                    
16.38/4.49	     [half](x0) = x0,
16.38/4.49	     
16.38/4.49	           [0]
16.38/4.49	     [0] = [0]
16.38/4.49	    orientation:
16.38/4.49	                 [0]    [0]      
16.38/4.49	     half(0()) = [0] >= [0] = 0()
16.38/4.49	     
16.38/4.49	                         [0]        [0]             
16.38/4.49	     half(s(s(x))) = x + [2] >= x + [1] = s(half(x))
16.38/4.49	     
16.38/4.49	                    [2 1]    [2]    [2 1]    [1]                     
16.38/4.49	     log(s(s(x))) = [1 1]x + [3] >= [1 1]x + [3] = s(log(s(half(x))))
16.38/4.49	     
16.38/4.49	               [2 0]     [2 0]              
16.38/4.49	     rand(x) = [2 0]x >= [2 0]x = rand(s(x))
16.38/4.49	    problem:
16.38/4.49	     strict:
16.38/4.49	      half(0()) -> 0()
16.38/4.49	      half(s(s(x))) -> s(half(x))
16.38/4.49	     weak:
16.38/4.49	      rand(x) -> rand(s(x))
16.38/4.49	    Arctic Interpretation Processor:
16.38/4.49	     dimension: 1
16.38/4.49	     interpretation:
16.38/4.49	      [rand](x0) = x0,
16.38/4.49	      
16.38/4.49	      [s](x0) = x0,
16.38/4.49	      
16.38/4.49	      [half](x0) = 2x0,
16.38/4.49	      
16.38/4.49	      [0] = 10
16.38/4.49	     orientation:
16.38/4.49	      half(0()) = 12 >= 10 = 0()
16.38/4.49	      
16.38/4.49	      half(s(s(x))) = 2x >= 2x = s(half(x))
16.38/4.49	      
16.38/4.49	      rand(x) = x >= x = rand(s(x))
16.38/4.49	     problem:
16.38/4.49	      strict:
16.38/4.49	       half(s(s(x))) -> s(half(x))
16.38/4.49	      weak:
16.38/4.49	       rand(x) -> rand(s(x))
16.38/4.49	     String Reversal Processor:
16.38/4.49	      strict:
16.38/4.49	       s(s(half(x))) -> half(s(x))
16.38/4.49	      weak:
16.38/4.49	       rand(x) -> s(rand(x))
16.38/4.49	      Arctic Interpretation Processor:
16.38/4.49	       dimension: 2
16.38/4.49	       interpretation:
16.38/4.49	                     [0  0 ]  
16.38/4.49	        [rand](x0) = [-& -&]x0,
16.38/4.49	        
16.38/4.49	                  [0  4 ]  
16.38/4.49	        [s](x0) = [-& 3 ]x0,
16.38/4.49	        
16.38/4.49	                     [6 6]  
16.38/4.49	        [half](x0) = [1 5]x0
16.38/4.49	       orientation:
16.38/4.49	                        [8  12]     [6  10]              
16.38/4.49	        s(s(half(x))) = [7  11]x >= [1  8 ]x = half(s(x))
16.38/4.49	        
16.38/4.49	                  [0  0 ]     [0  0 ]              
16.38/4.49	        rand(x) = [-& -&]x >= [-& -&]x = s(rand(x))
16.38/4.49	       problem:
16.38/4.49	        strict:
16.38/4.49	         
16.38/4.49	        weak:
16.38/4.49	         rand(x) -> s(rand(x))
16.38/4.49	       Qed
16.38/4.49	EOF