6.83/1.87	YES
6.83/1.87	
6.83/1.87	Problem:
6.83/1.87	 strict:
6.83/1.87	  g(s(x)) -> f(x)
6.83/1.87	  f(0()) -> s(0())
6.83/1.87	  f(s(x)) -> s(s(g(x)))
6.83/1.87	  g(0()) -> 0()
6.83/1.87	 weak:
6.83/1.87	  rand(x) -> x
6.83/1.87	  rand(x) -> rand(s(x))
6.83/1.87	
6.83/1.87	Proof:
6.83/1.87	 Arctic Interpretation Processor:
6.83/1.87	  dimension: 1
6.83/1.87	  interpretation:
6.83/1.87	   [rand](x0) = 2x0,
6.83/1.87	   
6.83/1.87	   [0] = 9,
6.83/1.87	   
6.83/1.87	   [f](x0) = 8x0,
6.83/1.87	   
6.83/1.87	   [g](x0) = 8x0,
6.83/1.87	   
6.83/1.87	   [s](x0) = x0
6.83/1.87	  orientation:
6.83/1.87	   g(s(x)) = 8x >= 8x = f(x)
6.83/1.87	   
6.83/1.87	   f(0()) = 17 >= 9 = s(0())
6.83/1.87	   
6.83/1.87	   f(s(x)) = 8x >= 8x = s(s(g(x)))
6.83/1.87	   
6.83/1.87	   g(0()) = 17 >= 9 = 0()
6.83/1.87	   
6.83/1.87	   rand(x) = 2x >= x = x
6.83/1.87	   
6.83/1.87	   rand(x) = 2x >= 2x = rand(s(x))
6.83/1.87	  problem:
6.83/1.87	   strict:
6.83/1.87	    g(s(x)) -> f(x)
6.83/1.87	    f(s(x)) -> s(s(g(x)))
6.83/1.87	   weak:
6.83/1.87	    rand(x) -> rand(s(x))
6.83/1.87	  Matrix Interpretation Processor: dim=2
6.83/1.87	   
6.83/1.87	   interpretation:
6.83/1.87	                 [1 0]  
6.83/1.87	    [rand](x0) = [0 0]x0,
6.83/1.87	    
6.83/1.87	              [1 2]     [1]
6.83/1.87	    [f](x0) = [0 1]x0 + [1],
6.83/1.87	    
6.83/1.87	              [1 2]  
6.83/1.87	    [g](x0) = [0 1]x0,
6.83/1.87	    
6.83/1.87	                   [0]
6.83/1.87	    [s](x0) = x0 + [1]
6.83/1.87	   orientation:
6.83/1.87	              [1 2]    [2]    [1 2]    [1]       
6.83/1.87	    g(s(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(x)
6.83/1.87	    
6.83/1.87	              [1 2]    [3]    [1 2]    [0]             
6.83/1.87	    f(s(x)) = [0 1]x + [2] >= [0 1]x + [2] = s(s(g(x)))
6.83/1.87	    
6.83/1.87	              [1 0]     [1 0]              
6.83/1.87	    rand(x) = [0 0]x >= [0 0]x = rand(s(x))
6.83/1.87	   problem:
6.83/1.87	    strict:
6.83/1.87	     
6.83/1.87	    weak:
6.83/1.87	     rand(x) -> rand(s(x))
6.83/1.87	   Qed
6.83/1.87	EOF