18.51/5.15	YES
18.51/5.16	
18.51/5.16	Problem:
18.51/5.16	 a(a(x1)) -> b(c(c(c(x1))))
18.51/5.16	 b(c(x1)) -> d(d(d(d(x1))))
18.51/5.16	 a(x1) -> d(c(d(x1)))
18.51/5.16	 b(b(x1)) -> c(c(c(x1)))
18.51/5.16	 c(c(x1)) -> d(d(d(x1)))
18.51/5.16	 c(d(d(x1))) -> a(x1)
18.51/5.16	
18.51/5.16	Proof:
18.51/5.16	 Matrix Interpretation Processor: dim=1
18.51/5.16	  
18.51/5.16	  interpretation:
18.51/5.16	   [d](x0) = x0 + 4,
18.51/5.16	   
18.51/5.16	   [b](x0) = x0 + 10,
18.51/5.16	   
18.51/5.16	   [c](x0) = x0 + 6,
18.51/5.16	   
18.51/5.16	   [a](x0) = x0 + 14
18.51/5.16	  orientation:
18.51/5.16	   a(a(x1)) = x1 + 28 >= x1 + 28 = b(c(c(c(x1))))
18.51/5.16	   
18.51/5.16	   b(c(x1)) = x1 + 16 >= x1 + 16 = d(d(d(d(x1))))
18.51/5.16	   
18.51/5.16	   a(x1) = x1 + 14 >= x1 + 14 = d(c(d(x1)))
18.51/5.16	   
18.51/5.16	   b(b(x1)) = x1 + 20 >= x1 + 18 = c(c(c(x1)))
18.51/5.16	   
18.51/5.16	   c(c(x1)) = x1 + 12 >= x1 + 12 = d(d(d(x1)))
18.51/5.16	   
18.51/5.16	   c(d(d(x1))) = x1 + 14 >= x1 + 14 = a(x1)
18.51/5.16	  problem:
18.51/5.16	   a(a(x1)) -> b(c(c(c(x1))))
18.51/5.16	   b(c(x1)) -> d(d(d(d(x1))))
18.51/5.16	   a(x1) -> d(c(d(x1)))
18.51/5.16	   c(c(x1)) -> d(d(d(x1)))
18.51/5.16	   c(d(d(x1))) -> a(x1)
18.51/5.16	  Matrix Interpretation Processor: dim=1
18.51/5.16	   
18.51/5.16	   interpretation:
18.51/5.16	    [d](x0) = x0 + 2,
18.51/5.16	    
18.51/5.16	    [b](x0) = x0,
18.51/5.16	    
18.51/5.16	    [c](x0) = x0 + 8,
18.51/5.16	    
18.51/5.16	    [a](x0) = x0 + 12
18.51/5.16	   orientation:
18.51/5.16	    a(a(x1)) = x1 + 24 >= x1 + 24 = b(c(c(c(x1))))
18.51/5.16	    
18.51/5.16	    b(c(x1)) = x1 + 8 >= x1 + 8 = d(d(d(d(x1))))
18.51/5.16	    
18.51/5.16	    a(x1) = x1 + 12 >= x1 + 12 = d(c(d(x1)))
18.51/5.16	    
18.51/5.16	    c(c(x1)) = x1 + 16 >= x1 + 6 = d(d(d(x1)))
18.51/5.16	    
18.51/5.16	    c(d(d(x1))) = x1 + 12 >= x1 + 12 = a(x1)
18.51/5.16	   problem:
18.51/5.16	    a(a(x1)) -> b(c(c(c(x1))))
18.51/5.16	    b(c(x1)) -> d(d(d(d(x1))))
18.51/5.16	    a(x1) -> d(c(d(x1)))
18.51/5.16	    c(d(d(x1))) -> a(x1)
18.51/5.16	   String Reversal Processor:
18.51/5.16	    a(a(x1)) -> c(c(c(b(x1))))
18.51/5.16	    c(b(x1)) -> d(d(d(d(x1))))
18.51/5.16	    a(x1) -> d(c(d(x1)))
18.51/5.16	    d(d(c(x1))) -> a(x1)
18.51/5.16	    Matrix Interpretation Processor: dim=3
18.51/5.16	     
18.51/5.16	     interpretation:
18.51/5.16	                [1 0 1]  
18.51/5.16	      [d](x0) = [0 0 0]x0
18.51/5.16	                [1 0 0]  ,
18.51/5.16	      
18.51/5.16	                [3 0 1]     [3]
18.51/5.16	      [b](x0) = [2 0 2]x0 + [0]
18.51/5.16	                [3 1 2]     [1],
18.51/5.16	      
18.51/5.16	                [1 1 0]     [1]
18.51/5.16	      [c](x0) = [0 0 0]x0 + [0]
18.51/5.16	                [0 0 1]     [0],
18.51/5.16	      
18.51/5.16	                [2 0 1]     [2]
18.51/5.16	      [a](x0) = [0 0 0]x0 + [0]
18.51/5.16	                [1 1 1]     [1]
18.51/5.16	     orientation:
18.51/5.16	                 [5 1 3]     [7]    [5 0 3]     [6]                 
18.51/5.16	      a(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c(c(b(x1))))
18.51/5.16	                 [3 1 2]     [4]    [3 1 2]     [1]                 
18.51/5.16	      
18.51/5.16	                 [5 0 3]     [4]    [5 0 3]                   
18.51/5.16	      c(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = d(d(d(d(x1))))
18.51/5.16	                 [3 1 2]     [1]    [3 0 2]                   
18.51/5.16	      
18.51/5.16	              [2 0 1]     [2]    [2 0 1]     [1]              
18.51/5.16	      a(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(c(d(x1)))
18.51/5.16	              [1 1 1]     [1]    [1 0 1]     [1]              
18.51/5.16	      
18.51/5.16	                    [2 2 1]     [2]    [2 0 1]     [2]        
18.51/5.16	      d(d(c(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(x1)
18.51/5.16	                    [1 1 1]     [1]    [1 1 1]     [1]        
18.51/5.16	     problem:
18.51/5.16	      d(d(c(x1))) -> a(x1)
18.51/5.16	     KBO Processor:
18.51/5.16	      weight function:
18.51/5.16	       w0 = 1
18.51/5.16	       w(c) = w(a) = 1
18.51/5.16	       w(d) = 0
18.51/5.16	      precedence:
18.51/5.16	       d > c ~ a
18.51/5.16	      problem:
18.51/5.16	       
18.51/5.16	      Qed
18.51/5.16	EOF