14.37/4.02	YES
14.37/4.02	
14.37/4.02	Problem:
14.37/4.02	 strict:
14.37/4.02	  f(c(s(x),y)) -> f(c(x,s(y)))
14.37/4.02	  f(c(s(x),s(y))) -> g(c(x,y))
14.37/4.02	  g(c(x,s(y))) -> g(c(s(x),y))
14.37/4.02	  g(c(s(x),s(y))) -> f(c(x,y))
14.37/4.02	 weak:
14.37/4.02	  rand(x) -> x
14.37/4.02	  rand(x) -> rand(s(x))
14.37/4.02	
14.37/4.02	Proof:
14.37/4.02	 Matrix Interpretation Processor: dim=2
14.37/4.02	  
14.37/4.02	  interpretation:
14.37/4.02	                [2 0]     [1]
14.37/4.02	   [rand](x0) = [0 2]x0 + [0],
14.37/4.02	   
14.37/4.02	             [2 1]  
14.37/4.02	   [g](x0) = [2 0]x0,
14.37/4.02	   
14.37/4.02	             [2 1]  
14.37/4.02	   [f](x0) = [2 0]x0,
14.37/4.02	   
14.37/4.02	                 [1 0]     [1 1]     [0]
14.37/4.02	   [c](x0, x1) = [0 2]x0 + [0 0]x1 + [2],
14.37/4.02	   
14.37/4.02	               
14.37/4.02	   [s](x0) = x0
14.37/4.02	  orientation:
14.37/4.02	                  [2 2]    [2 2]    [2]    [2 2]    [2 2]    [2]               
14.37/4.02	   f(c(s(x),y)) = [2 0]x + [2 2]y + [0] >= [2 0]x + [2 2]y + [0] = f(c(x,s(y)))
14.37/4.02	   
14.37/4.02	                     [2 2]    [2 2]    [2]    [2 2]    [2 2]    [2]            
14.37/4.02	   f(c(s(x),s(y))) = [2 0]x + [2 2]y + [0] >= [2 0]x + [2 2]y + [0] = g(c(x,y))
14.37/4.02	   
14.37/4.02	                  [2 2]    [2 2]    [2]    [2 2]    [2 2]    [2]               
14.37/4.02	   g(c(x,s(y))) = [2 0]x + [2 2]y + [0] >= [2 0]x + [2 2]y + [0] = g(c(s(x),y))
14.37/4.02	   
14.37/4.02	                     [2 2]    [2 2]    [2]    [2 2]    [2 2]    [2]            
14.37/4.02	   g(c(s(x),s(y))) = [2 0]x + [2 2]y + [0] >= [2 0]x + [2 2]y + [0] = f(c(x,y))
14.37/4.02	   
14.37/4.02	             [2 0]    [1]         
14.37/4.02	   rand(x) = [0 2]x + [0] >= x = x
14.37/4.02	   
14.37/4.02	             [2 0]    [1]    [2 0]    [1]             
14.37/4.02	   rand(x) = [0 2]x + [0] >= [0 2]x + [0] = rand(s(x))
14.37/4.02	  problem:
14.37/4.02	   strict:
14.37/4.02	    f(c(s(x),y)) -> f(c(x,s(y)))
14.37/4.02	    f(c(s(x),s(y))) -> g(c(x,y))
14.37/4.02	    g(c(x,s(y))) -> g(c(s(x),y))
14.37/4.02	    g(c(s(x),s(y))) -> f(c(x,y))
14.37/4.02	   weak:
14.37/4.02	    rand(x) -> rand(s(x))
14.37/4.02	  Matrix Interpretation Processor: dim=2
14.37/4.02	   
14.37/4.02	   interpretation:
14.37/4.02	                 [2 0]  
14.37/4.02	    [rand](x0) = [0 0]x0,
14.37/4.02	    
14.37/4.02	              [1 1]  
14.37/4.02	    [g](x0) = [1 1]x0,
14.37/4.02	    
14.37/4.02	              [1 1]  
14.37/4.02	    [f](x0) = [1 1]x0,
14.37/4.02	    
14.37/4.02	                  [2 1]     [2 0]     [1]
14.37/4.02	    [c](x0, x1) = [0 0]x0 + [0 1]x1 + [0],
14.37/4.02	    
14.37/4.02	                   [0]
14.37/4.02	    [s](x0) = x0 + [1]
14.37/4.02	   orientation:
14.37/4.02	                   [2 1]    [2 1]    [2]    [2 1]    [2 1]    [2]               
14.37/4.02	    f(c(s(x),y)) = [2 1]x + [2 1]y + [2] >= [2 1]x + [2 1]y + [2] = f(c(x,s(y)))
14.37/4.02	    
14.37/4.02	                      [2 1]    [2 1]    [3]    [2 1]    [2 1]    [1]            
14.37/4.02	    f(c(s(x),s(y))) = [2 1]x + [2 1]y + [3] >= [2 1]x + [2 1]y + [1] = g(c(x,y))
14.37/4.02	    
14.37/4.02	                   [2 1]    [2 1]    [2]    [2 1]    [2 1]    [2]               
14.37/4.02	    g(c(x,s(y))) = [2 1]x + [2 1]y + [2] >= [2 1]x + [2 1]y + [2] = g(c(s(x),y))
14.37/4.02	    
14.37/4.02	                      [2 1]    [2 1]    [3]    [2 1]    [2 1]    [1]            
14.37/4.02	    g(c(s(x),s(y))) = [2 1]x + [2 1]y + [3] >= [2 1]x + [2 1]y + [1] = f(c(x,y))
14.37/4.02	    
14.37/4.02	              [2 0]     [2 0]              
14.37/4.02	    rand(x) = [0 0]x >= [0 0]x = rand(s(x))
14.37/4.02	   problem:
14.37/4.02	    strict:
14.37/4.02	     f(c(s(x),y)) -> f(c(x,s(y)))
14.37/4.02	     g(c(x,s(y))) -> g(c(s(x),y))
14.37/4.02	    weak:
14.37/4.02	     rand(x) -> rand(s(x))
14.37/4.02	   Bounds Processor:
14.37/4.02	    bound: 1
14.37/4.02	    enrichment: match-rt
14.37/4.02	    automaton:
14.37/4.02	     final states: {6}
14.37/4.02	     transitions:
14.37/4.02	      f1(10) -> 6*
14.37/4.02	      c1(6,9) -> 10*
14.37/4.02	      s1(9) -> 9*
14.37/4.02	      s1(6) -> 9*
14.37/4.02	      rand1(9) -> 6*
14.37/4.02	      f0(6) -> 6*
14.37/4.02	      c0(6,6) -> 6*
14.37/4.02	      s0(6) -> 6*
14.37/4.02	      g0(6) -> 6*
14.37/4.02	      rand0(6) -> 6*
14.37/4.02	    problem:
14.37/4.02	     strict:
14.37/4.02	      g(c(x,s(y))) -> g(c(s(x),y))
14.37/4.02	     weak:
14.37/4.02	      rand(x) -> rand(s(x))
14.37/4.02	    Bounds Processor:
14.37/4.02	     bound: 1
14.37/4.02	     enrichment: match-rt
14.37/4.02	     automaton:
14.37/4.02	      final states: {5}
14.37/4.02	      transitions:
14.37/4.02	       g0(5) -> 5*
14.37/4.02	       rand0(5) -> 5*
14.37/4.02	       c1(8,5) -> 9*
14.37/4.02	       s1(5) -> 8*
14.37/4.02	       s1(12) -> 13*
14.37/4.02	       s1(8) -> 8*
14.37/4.02	       g1(9) -> 5*
14.37/4.02	       rand1(10) -> 11*
14.37/4.02	       c0(5,5) -> 5*
14.37/4.02	       s0(5) -> 5*
14.37/4.02	       8 -> 10*
14.37/4.02	       10 -> 12*
14.37/4.02	       11 -> 5*
14.37/4.02	       13 -> 10*
14.37/4.02	     problem:
14.37/4.02	      strict:
14.37/4.02	       
14.37/4.02	      weak:
14.37/4.02	       rand(x) -> rand(s(x))
14.37/4.02	     Qed
14.37/4.03	EOF