17.77/4.95	YES
17.77/4.96	
17.77/4.96	Problem:
17.77/4.96	 strict:
17.77/4.96	  g(c(x,s(y))) -> g(c(s(x),y))
17.77/4.96	  f(c(s(x),y)) -> f(c(x,s(y)))
17.77/4.96	  f(f(x)) -> f(d(f(x)))
17.77/4.96	  f(x) -> x
17.77/4.96	 weak:
17.77/4.96	  rand(x) -> x
17.77/4.96	  rand(x) -> rand(s(x))
17.77/4.96	
17.77/4.96	Proof:
17.77/4.96	 Matrix Interpretation Processor: dim=2
17.77/4.96	  
17.77/4.96	  interpretation:
17.77/4.96	                [1 0]     [0]
17.77/4.96	   [rand](x0) = [0 2]x0 + [1],
17.77/4.96	   
17.77/4.96	             [1 0]  
17.77/4.96	   [d](x0) = [0 0]x0,
17.77/4.96	   
17.77/4.96	                  [1]
17.77/4.96	   [f](x0) = x0 + [0],
17.77/4.96	   
17.77/4.96	             [2 0]     [2]
17.77/4.96	   [g](x0) = [2 0]x0 + [1],
17.77/4.96	   
17.77/4.96	                 [1 0]     [1 0]  
17.77/4.96	   [c](x0, x1) = [0 0]x0 + [0 2]x1,
17.77/4.96	   
17.77/4.96	             [1 0]  
17.77/4.96	   [s](x0) = [0 0]x0
17.77/4.96	  orientation:
17.77/4.96	                  [2 0]    [2 0]    [2]    [2 0]    [2 0]    [2]               
17.77/4.96	   g(c(x,s(y))) = [2 0]x + [2 0]y + [1] >= [2 0]x + [2 0]y + [1] = g(c(s(x),y))
17.77/4.96	   
17.77/4.96	                  [1 0]    [1 0]    [1]    [1 0]    [1 0]    [1]               
17.77/4.96	   f(c(s(x),y)) = [0 0]x + [0 2]y + [0] >= [0 0]x + [0 0]y + [0] = f(c(x,s(y)))
17.77/4.96	   
17.77/4.96	                 [2]    [1 0]    [2]             
17.77/4.96	   f(f(x)) = x + [0] >= [0 0]x + [0] = f(d(f(x)))
17.77/4.96	   
17.77/4.96	              [1]         
17.77/4.96	   f(x) = x + [0] >= x = x
17.77/4.96	   
17.77/4.96	             [1 0]    [0]         
17.77/4.96	   rand(x) = [0 2]x + [1] >= x = x
17.77/4.96	   
17.77/4.96	             [1 0]    [0]    [1 0]    [0]             
17.77/4.96	   rand(x) = [0 2]x + [1] >= [0 0]x + [1] = rand(s(x))
17.77/4.96	  problem:
17.77/4.96	   strict:
17.77/4.96	    g(c(x,s(y))) -> g(c(s(x),y))
17.77/4.96	    f(c(s(x),y)) -> f(c(x,s(y)))
17.77/4.96	    f(f(x)) -> f(d(f(x)))
17.77/4.96	   weak:
17.77/4.96	    rand(x) -> x
17.77/4.96	    rand(x) -> rand(s(x))
17.77/4.96	  Matrix Interpretation Processor: dim=2
17.77/4.96	   
17.77/4.96	   interpretation:
17.77/4.96	                 [2 0]     [1]
17.77/4.96	    [rand](x0) = [2 1]x0 + [1],
17.77/4.96	    
17.77/4.96	              [1 0]  
17.77/4.96	    [d](x0) = [0 0]x0,
17.77/4.96	    
17.77/4.96	              [1 1]  
17.77/4.96	    [f](x0) = [1 1]x0,
17.77/4.96	    
17.77/4.96	              [1 0]     [3]
17.77/4.96	    [g](x0) = [2 0]x0 + [0],
17.77/4.96	    
17.77/4.96	                  [1 0]     [1 0]     [0]
17.77/4.96	    [c](x0, x1) = [2 2]x0 + [0 0]x1 + [1],
17.77/4.96	    
17.77/4.96	                
17.77/4.96	    [s](x0) = x0
17.77/4.96	   orientation:
17.77/4.96	                   [1 0]    [1 0]    [3]    [1 0]    [1 0]    [3]               
17.77/4.96	    g(c(x,s(y))) = [2 0]x + [2 0]y + [0] >= [2 0]x + [2 0]y + [0] = g(c(s(x),y))
17.77/4.96	    
17.77/4.96	                   [3 2]    [1 0]    [1]    [3 2]    [1 0]    [1]               
17.77/4.96	    f(c(s(x),y)) = [3 2]x + [1 0]y + [1] >= [3 2]x + [1 0]y + [1] = f(c(x,s(y)))
17.77/4.96	    
17.77/4.96	              [2 2]     [1 1]              
17.77/4.96	    f(f(x)) = [2 2]x >= [1 1]x = f(d(f(x)))
17.77/4.96	    
17.77/4.96	              [2 0]    [1]         
17.77/4.96	    rand(x) = [2 1]x + [1] >= x = x
17.77/4.96	    
17.77/4.96	              [2 0]    [1]    [2 0]    [1]             
17.77/4.96	    rand(x) = [2 1]x + [1] >= [2 1]x + [1] = rand(s(x))
17.77/4.96	   problem:
17.77/4.96	    strict:
17.77/4.96	     g(c(x,s(y))) -> g(c(s(x),y))
17.77/4.96	     f(c(s(x),y)) -> f(c(x,s(y)))
17.77/4.96	     f(f(x)) -> f(d(f(x)))
17.77/4.96	    weak:
17.77/4.96	     rand(x) -> rand(s(x))
17.77/4.96	   Bounds Processor:
17.77/4.96	    bound: 1
17.77/4.96	    enrichment: match-rt
17.77/4.96	    automaton:
17.77/4.96	     final states: {7}
17.77/4.96	     transitions:
17.77/4.96	      c1(7,14) -> 15*
17.77/4.96	      s1(7) -> 14*
17.77/4.96	      s1(14) -> 14*
17.77/4.96	      f1(15) -> 7*
17.77/4.96	      f1(7) -> 7*
17.77/4.96	      d1(7) -> 15*
17.77/4.96	      g0(7) -> 7*
17.77/4.96	      rand1(14) -> 7*
17.77/4.96	      c0(7,7) -> 7*
17.77/4.96	      s0(7) -> 7*
17.77/4.96	      f0(7) -> 7*
17.77/4.96	      d0(7) -> 7*
17.77/4.96	      rand0(7) -> 7*
17.77/4.96	    problem:
17.77/4.96	     strict:
17.77/4.96	      g(c(x,s(y))) -> g(c(s(x),y))
17.77/4.96	      f(f(x)) -> f(d(f(x)))
17.77/4.96	     weak:
17.77/4.96	      rand(x) -> rand(s(x))
17.77/4.96	    Matrix Interpretation Processor: dim=2
17.77/4.96	     
17.77/4.96	     interpretation:
17.77/4.96	                   [1 0]  
17.77/4.96	      [rand](x0) = [0 0]x0,
17.77/4.96	      
17.77/4.96	                     [0]
17.77/4.96	      [d](x0) = x0 + [1],
17.77/4.96	      
17.77/4.96	                [1 0]     [0]
17.77/4.96	      [f](x0) = [0 0]x0 + [1],
17.77/4.96	      
17.77/4.96	                [1 1]  
17.77/4.96	      [g](x0) = [2 0]x0,
17.77/4.96	      
17.77/4.96	                    [1 0]     [1 0]  
17.77/4.96	      [c](x0, x1) = [2 0]x0 + [2 1]x1,
17.77/4.96	      
17.77/4.96	                [1 0]     [0]
17.77/4.96	      [s](x0) = [0 2]x0 + [1]
17.77/4.96	     orientation:
17.77/4.96	                     [3 0]    [3 2]    [1]    [3 0]    [3 1]                
17.77/4.96	      g(c(x,s(y))) = [2 0]x + [2 0]y + [0] >= [2 0]x + [2 0]y = g(c(s(x),y))
17.77/4.96	      
17.77/4.96	                [1 0]    [0]    [1 0]    [0]             
17.77/4.96	      f(f(x)) = [0 0]x + [1] >= [0 0]x + [1] = f(d(f(x)))
17.77/4.96	      
17.77/4.96	                [1 0]     [1 0]              
17.77/4.96	      rand(x) = [0 0]x >= [0 0]x = rand(s(x))
17.77/4.96	     problem:
17.77/4.96	      strict:
17.77/4.96	       f(f(x)) -> f(d(f(x)))
17.77/4.96	      weak:
17.77/4.96	       rand(x) -> rand(s(x))
17.77/4.96	     Arctic Interpretation Processor:
17.77/4.96	      dimension: 2
17.77/4.96	      interpretation:
17.77/4.96	                    [0 0]  
17.77/4.96	       [rand](x0) = [4 1]x0,
17.77/4.96	       
17.77/4.96	                 [1  0 ]  
17.77/4.96	       [d](x0) = [0  -&]x0,
17.77/4.96	       
17.77/4.96	                 [0 2]  
17.77/4.96	       [f](x0) = [2 6]x0,
17.77/4.96	       
17.77/4.96	                 [0  -&]  
17.77/4.96	       [s](x0) = [0  0 ]x0
17.77/4.96	      orientation:
17.77/4.96	                 [4  8 ]     [2 6]              
17.77/4.96	       f(f(x)) = [8  12]x >= [6 8]x = f(d(f(x)))
17.77/4.96	       
17.77/4.96	                 [0 0]     [0 0]              
17.77/4.96	       rand(x) = [4 1]x >= [4 1]x = rand(s(x))
17.77/4.96	      problem:
17.77/4.96	       strict:
17.77/4.96	        
17.77/4.96	       weak:
17.77/4.96	        rand(x) -> rand(s(x))
17.77/4.96	      Qed
17.77/4.96	EOF