21.36/5.83	YES
21.71/5.84	
21.71/5.84	Problem:
21.71/5.84	 strict:
21.71/5.84	  p(s(x1)) -> s(x1)
21.71/5.84	  n(s(x1)) -> s(x1)
21.71/5.84	  o(s(x1)) -> s(x1)
21.71/5.84	  o(n(x1)) -> n(o(x1))
21.71/5.84	  o(m(x1)) -> n(o(x1))
21.71/5.84	  n(o(p(x1))) -> o(n(x1))
21.71/5.84	 weak:
21.71/5.84	  t(x1) -> t(c(n(x1)))
21.71/5.84	  p(n(x1)) -> m(p(x1))
21.71/5.84	  p(m(x1)) -> m(p(x1))
21.71/5.84	  n(p(x1)) -> p(n(x1))
21.71/5.84	  c(p(x1)) -> p(c(x1))
21.71/5.84	  c(m(x1)) -> m(c(x1))
21.71/5.84	  c(n(x1)) -> n(c(x1))
21.71/5.84	  c(o(x1)) -> o(c(x1))
21.71/5.84	  c(o(x1)) -> o(x1)
21.71/5.84	
21.71/5.84	Proof:
21.71/5.84	 Arctic Interpretation Processor:
21.71/5.84	  dimension: 1
21.71/5.84	  interpretation:
21.71/5.84	   [c](x0) = x0,
21.71/5.84	   
21.71/5.84	   [t](x0) = x0,
21.71/5.84	   
21.71/5.84	   [m](x0) = x0,
21.71/5.84	   
21.71/5.84	   [o](x0) = 8x0,
21.71/5.84	   
21.71/5.84	   [n](x0) = x0,
21.71/5.84	   
21.71/5.84	   [p](x0) = 14x0,
21.71/5.84	   
21.71/5.84	   [s](x0) = x0
21.71/5.84	  orientation:
21.71/5.84	   p(s(x1)) = 14x1 >= x1 = s(x1)
21.71/5.84	   
21.71/5.84	   n(s(x1)) = x1 >= x1 = s(x1)
21.71/5.84	   
21.71/5.84	   o(s(x1)) = 8x1 >= x1 = s(x1)
21.71/5.84	   
21.71/5.84	   o(n(x1)) = 8x1 >= 8x1 = n(o(x1))
21.71/5.84	   
21.71/5.84	   o(m(x1)) = 8x1 >= 8x1 = n(o(x1))
21.71/5.84	   
21.71/5.84	   n(o(p(x1))) = 22x1 >= 8x1 = o(n(x1))
21.71/5.84	   
21.71/5.84	   t(x1) = x1 >= x1 = t(c(n(x1)))
21.71/5.84	   
21.71/5.84	   p(n(x1)) = 14x1 >= 14x1 = m(p(x1))
21.71/5.84	   
21.71/5.84	   p(m(x1)) = 14x1 >= 14x1 = m(p(x1))
21.71/5.84	   
21.71/5.84	   n(p(x1)) = 14x1 >= 14x1 = p(n(x1))
21.71/5.84	   
21.71/5.84	   c(p(x1)) = 14x1 >= 14x1 = p(c(x1))
21.71/5.84	   
21.71/5.84	   c(m(x1)) = x1 >= x1 = m(c(x1))
21.71/5.84	   
21.71/5.84	   c(n(x1)) = x1 >= x1 = n(c(x1))
21.71/5.84	   
21.71/5.84	   c(o(x1)) = 8x1 >= 8x1 = o(c(x1))
21.71/5.84	   
21.71/5.84	   c(o(x1)) = 8x1 >= 8x1 = o(x1)
21.71/5.84	  problem:
21.71/5.84	   strict:
21.71/5.84	    n(s(x1)) -> s(x1)
21.71/5.84	    o(n(x1)) -> n(o(x1))
21.71/5.84	    o(m(x1)) -> n(o(x1))
21.71/5.84	   weak:
21.71/5.84	    t(x1) -> t(c(n(x1)))
21.71/5.84	    p(n(x1)) -> m(p(x1))
21.71/5.84	    p(m(x1)) -> m(p(x1))
21.71/5.84	    n(p(x1)) -> p(n(x1))
21.71/5.84	    c(p(x1)) -> p(c(x1))
21.71/5.84	    c(m(x1)) -> m(c(x1))
21.71/5.84	    c(n(x1)) -> n(c(x1))
21.71/5.84	    c(o(x1)) -> o(c(x1))
21.71/5.84	    c(o(x1)) -> o(x1)
21.71/5.84	  Matrix Interpretation Processor: dim=2
21.71/5.84	   
21.71/5.84	   interpretation:
21.71/5.84	                
21.71/5.84	    [c](x0) = x0,
21.71/5.84	    
21.71/5.84	              [2 0]     [2]
21.71/5.84	    [t](x0) = [2 0]x0 + [0],
21.71/5.84	    
21.71/5.84	              [1 0]     [0]
21.71/5.84	    [m](x0) = [0 2]x0 + [2],
21.71/5.84	    
21.71/5.84	              [1 1]  
21.71/5.84	    [o](x0) = [0 1]x0,
21.71/5.84	    
21.71/5.84	              [1 0]     [0]
21.71/5.84	    [n](x0) = [0 2]x0 + [2],
21.71/5.84	    
21.71/5.84	                
21.71/5.84	    [p](x0) = x0,
21.71/5.84	    
21.71/5.84	              [1 0]     [1]
21.71/5.84	    [s](x0) = [1 0]x0 + [0]
21.71/5.84	   orientation:
21.71/5.84	               [1 0]     [1]    [1 0]     [1]        
21.71/5.84	    n(s(x1)) = [2 0]x1 + [2] >= [1 0]x1 + [0] = s(x1)
21.71/5.84	    
21.71/5.84	               [1 2]     [2]    [1 1]     [0]           
21.71/5.84	    o(n(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = n(o(x1))
21.71/5.84	    
21.71/5.84	               [1 2]     [2]    [1 1]     [0]           
21.71/5.84	    o(m(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = n(o(x1))
21.71/5.84	    
21.71/5.84	            [2 0]     [2]    [2 0]     [2]              
21.71/5.84	    t(x1) = [2 0]x1 + [0] >= [2 0]x1 + [0] = t(c(n(x1)))
21.71/5.84	    
21.71/5.84	               [1 0]     [0]    [1 0]     [0]           
21.71/5.84	    p(n(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = m(p(x1))
21.71/5.84	    
21.71/5.84	               [1 0]     [0]    [1 0]     [0]           
21.71/5.84	    p(m(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = m(p(x1))
21.71/5.84	    
21.71/5.84	               [1 0]     [0]    [1 0]     [0]           
21.71/5.84	    n(p(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = p(n(x1))
21.71/5.84	    
21.71/5.84	                                  
21.71/5.84	    c(p(x1)) = x1 >= x1 = p(c(x1))
21.71/5.84	    
21.71/5.84	               [1 0]     [0]    [1 0]     [0]           
21.71/5.84	    c(m(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = m(c(x1))
21.71/5.84	    
21.71/5.84	               [1 0]     [0]    [1 0]     [0]           
21.71/5.84	    c(n(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = n(c(x1))
21.71/5.84	    
21.71/5.84	               [1 1]      [1 1]             
21.71/5.84	    c(o(x1)) = [0 1]x1 >= [0 1]x1 = o(c(x1))
21.71/5.84	    
21.71/5.84	               [1 1]      [1 1]          
21.71/5.84	    c(o(x1)) = [0 1]x1 >= [0 1]x1 = o(x1)
21.71/5.84	   problem:
21.71/5.84	    strict:
21.71/5.84	     n(s(x1)) -> s(x1)
21.71/5.84	    weak:
21.71/5.84	     t(x1) -> t(c(n(x1)))
21.71/5.84	     p(n(x1)) -> m(p(x1))
21.71/5.84	     p(m(x1)) -> m(p(x1))
21.71/5.84	     n(p(x1)) -> p(n(x1))
21.71/5.84	     c(p(x1)) -> p(c(x1))
21.71/5.84	     c(m(x1)) -> m(c(x1))
21.71/5.84	     c(n(x1)) -> n(c(x1))
21.71/5.84	     c(o(x1)) -> o(c(x1))
21.71/5.84	     c(o(x1)) -> o(x1)
21.71/5.84	   Matrix Interpretation Processor: dim=2
21.71/5.84	    
21.71/5.84	    interpretation:
21.71/5.84	               [1 0]  
21.71/5.84	     [c](x0) = [0 0]x0,
21.71/5.84	     
21.71/5.84	               [1 2]     [2]
21.71/5.84	     [t](x0) = [0 2]x0 + [2],
21.71/5.84	     
21.71/5.84	               [1 0]  
21.71/5.84	     [m](x0) = [0 0]x0,
21.71/5.84	     
21.71/5.84	               [2 1]  
21.71/5.84	     [o](x0) = [0 0]x0,
21.71/5.84	     
21.71/5.84	               [1 2]  
21.71/5.84	     [n](x0) = [0 2]x0,
21.71/5.84	     
21.71/5.84	                 
21.71/5.84	     [p](x0) = x0,
21.71/5.84	     
21.71/5.84	               [1 2]     [0]
21.71/5.84	     [s](x0) = [0 0]x0 + [1]
21.71/5.84	    orientation:
21.71/5.84	                [1 2]     [2]    [1 2]     [0]        
21.71/5.84	     n(s(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = s(x1)
21.71/5.84	     
21.71/5.84	             [1 2]     [2]    [1 2]     [2]              
21.71/5.84	     t(x1) = [0 2]x1 + [2] >= [0 0]x1 + [2] = t(c(n(x1)))
21.71/5.84	     
21.71/5.84	                [1 2]      [1 0]             
21.71/5.84	     p(n(x1)) = [0 2]x1 >= [0 0]x1 = m(p(x1))
21.71/5.84	     
21.71/5.84	                [1 0]      [1 0]             
21.71/5.84	     p(m(x1)) = [0 0]x1 >= [0 0]x1 = m(p(x1))
21.71/5.84	     
21.71/5.84	                [1 2]      [1 2]             
21.71/5.84	     n(p(x1)) = [0 2]x1 >= [0 2]x1 = p(n(x1))
21.71/5.84	     
21.71/5.84	                [1 0]      [1 0]             
21.71/5.84	     c(p(x1)) = [0 0]x1 >= [0 0]x1 = p(c(x1))
21.71/5.84	     
21.71/5.84	                [1 0]      [1 0]             
21.71/5.84	     c(m(x1)) = [0 0]x1 >= [0 0]x1 = m(c(x1))
21.71/5.84	     
21.71/5.84	                [1 2]      [1 0]             
21.71/5.84	     c(n(x1)) = [0 0]x1 >= [0 0]x1 = n(c(x1))
21.71/5.84	     
21.71/5.84	                [2 1]      [2 0]             
21.71/5.84	     c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(c(x1))
21.71/5.84	     
21.71/5.84	                [2 1]      [2 1]          
21.71/5.84	     c(o(x1)) = [0 0]x1 >= [0 0]x1 = o(x1)
21.71/5.84	    problem:
21.71/5.84	     strict:
21.71/5.84	      
21.71/5.84	     weak:
21.71/5.84	      t(x1) -> t(c(n(x1)))
21.71/5.84	      p(n(x1)) -> m(p(x1))
21.71/5.84	      p(m(x1)) -> m(p(x1))
21.71/5.84	      n(p(x1)) -> p(n(x1))
21.71/5.84	      c(p(x1)) -> p(c(x1))
21.71/5.84	      c(m(x1)) -> m(c(x1))
21.71/5.84	      c(n(x1)) -> n(c(x1))
21.71/5.84	      c(o(x1)) -> o(c(x1))
21.71/5.84	      c(o(x1)) -> o(x1)
21.71/5.84	    Qed
21.71/5.85	EOF