170.02/43.27	YES
170.02/43.28	
170.02/43.28	Problem:
170.02/43.28	 a(a(x1)) -> b(b(x1))
170.02/43.28	 c(c(b(x1))) -> d(c(a(x1)))
170.02/43.28	 a(x1) -> d(c(c(x1)))
170.02/43.28	 c(d(x1)) -> b(c(x1))
170.02/43.28	
170.02/43.28	Proof:
170.02/43.28	 String Reversal Processor:
170.02/43.28	  a(a(x1)) -> b(b(x1))
170.02/43.28	  b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	  a(x1) -> c(c(d(x1)))
170.02/43.28	  d(c(x1)) -> c(b(x1))
170.02/43.28	  Matrix Interpretation Processor: dim=3
170.02/43.28	   
170.02/43.28	   interpretation:
170.02/43.28	              [1 0 0]     [0]
170.02/43.28	    [d](x0) = [0 0 1]x0 + [0]
170.02/43.28	              [0 0 0]     [1],
170.02/43.28	    
170.02/43.28	              [1 0 0]  
170.02/43.28	    [c](x0) = [0 0 0]x0
170.02/43.28	              [0 0 1]  ,
170.02/43.28	    
170.02/43.28	              [1 0 0]     [0]
170.02/43.28	    [b](x0) = [1 0 0]x0 + [1]
170.02/43.28	              [0 0 0]     [1],
170.02/43.28	    
170.02/43.28	              [1 1 0]     [0]
170.02/43.28	    [a](x0) = [1 1 0]x0 + [1]
170.02/43.28	              [0 1 0]     [1]
170.02/43.28	   orientation:
170.02/43.28	               [2 2 0]     [1]    [1 0 0]     [0]           
170.02/43.28	    a(a(x1)) = [2 2 0]x1 + [2] >= [1 0 0]x1 + [1] = b(b(x1))
170.02/43.28	               [1 1 0]     [2]    [0 0 0]     [1]           
170.02/43.28	    
170.02/43.28	                  [1 0 0]     [0]    [1 0 0]     [0]              
170.02/43.28	    b(c(c(x1))) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = a(c(d(x1)))
170.02/43.28	                  [0 0 0]     [1]    [0 0 0]     [1]              
170.02/43.28	    
170.02/43.28	            [1 1 0]     [0]    [1 0 0]     [0]              
170.02/43.28	    a(x1) = [1 1 0]x1 + [1] >= [0 0 0]x1 + [0] = c(c(d(x1)))
170.02/43.28	            [0 1 0]     [1]    [0 0 0]     [1]              
170.02/43.28	    
170.02/43.28	               [1 0 0]     [0]    [1 0 0]     [0]           
170.02/43.28	    d(c(x1)) = [0 0 1]x1 + [0] >= [0 0 0]x1 + [0] = c(b(x1))
170.02/43.28	               [0 0 0]     [1]    [0 0 0]     [1]           
170.02/43.28	   problem:
170.02/43.28	    b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	    a(x1) -> c(c(d(x1)))
170.02/43.28	    d(c(x1)) -> c(b(x1))
170.02/43.28	   DP Processor:
170.02/43.28	    DPs:
170.02/43.28	     b#(c(c(x1))) -> d#(x1)
170.02/43.28	     b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	     a#(x1) -> d#(x1)
170.02/43.28	     d#(c(x1)) -> b#(x1)
170.02/43.28	    TRS:
170.02/43.28	     b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	     a(x1) -> c(c(d(x1)))
170.02/43.28	     d(c(x1)) -> c(b(x1))
170.02/43.28	    TDG Processor:
170.02/43.28	     DPs:
170.02/43.28	      b#(c(c(x1))) -> d#(x1)
170.02/43.28	      b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	      a#(x1) -> d#(x1)
170.02/43.28	      d#(c(x1)) -> b#(x1)
170.02/43.28	     TRS:
170.02/43.28	      b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	      a(x1) -> c(c(d(x1)))
170.02/43.28	      d(c(x1)) -> c(b(x1))
170.02/43.28	     graph:
170.02/43.28	      a#(x1) -> d#(x1) -> d#(c(x1)) -> b#(x1)
170.02/43.28	      d#(c(x1)) -> b#(x1) -> b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	      d#(c(x1)) -> b#(x1) -> b#(c(c(x1))) -> d#(x1)
170.02/43.28	      b#(c(c(x1))) -> a#(c(d(x1))) -> a#(x1) -> d#(x1)
170.02/43.28	      b#(c(c(x1))) -> d#(x1) -> d#(c(x1)) -> b#(x1)
170.02/43.28	     Matrix Interpretation Processor: dim=3
170.02/43.28	      
170.02/43.28	      interpretation:
170.02/43.28	       [a#](x0) = [0 1 0]x0 + [1],
170.02/43.28	       
170.02/43.28	       [d#](x0) = [0 1 0]x0,
170.02/43.28	       
170.02/43.28	       [b#](x0) = [0 0 1]x0,
170.02/43.28	       
170.02/43.28	                 [0 1 0]     [1]
170.02/43.28	       [d](x0) = [0 1 0]x0 + [0]
170.02/43.28	                 [0 1 0]     [0],
170.02/43.28	       
170.02/43.28	                 [0 1 0]     [1]
170.02/43.28	       [c](x0) = [0 0 1]x0 + [0]
170.02/43.28	                 [1 0 0]     [0],
170.02/43.28	       
170.02/43.28	                 [0 0 1]  
170.02/43.28	       [b](x0) = [0 0 1]x0
170.02/43.28	                 [0 0 1]  ,
170.02/43.28	       
170.02/43.28	                 [0 1 0]     [1]
170.02/43.28	       [a](x0) = [0 1 0]x0 + [1]
170.02/43.28	                 [0 1 0]     [1]
170.02/43.28	      orientation:
170.02/43.28	       b#(c(c(x1))) = [0 1 0]x1 + [1] >= [0 1 0]x1 = d#(x1)
170.02/43.28	       
170.02/43.28	       b#(c(c(x1))) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = a#(c(d(x1)))
170.02/43.28	       
170.02/43.28	       a#(x1) = [0 1 0]x1 + [1] >= [0 1 0]x1 = d#(x1)
170.02/43.28	       
170.02/43.28	       d#(c(x1)) = [0 0 1]x1 >= [0 0 1]x1 = b#(x1)
170.02/43.28	       
170.02/43.28	                     [0 1 0]     [1]    [0 1 0]     [1]              
170.02/43.28	       b(c(c(x1))) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = a(c(d(x1)))
170.02/43.28	                     [0 1 0]     [1]    [0 1 0]     [1]              
170.02/43.28	       
170.02/43.28	               [0 1 0]     [1]    [0 1 0]     [1]              
170.02/43.28	       a(x1) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = c(c(d(x1)))
170.02/43.28	               [0 1 0]     [1]    [0 1 0]     [1]              
170.02/43.28	       
170.02/43.28	                  [0 0 1]     [1]    [0 0 1]     [1]           
170.02/43.28	       d(c(x1)) = [0 0 1]x1 + [0] >= [0 0 1]x1 + [0] = c(b(x1))
170.02/43.28	                  [0 0 1]     [0]    [0 0 1]     [0]           
170.02/43.28	      problem:
170.02/43.28	       DPs:
170.02/43.28	        b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	        d#(c(x1)) -> b#(x1)
170.02/43.28	       TRS:
170.02/43.28	        b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	        a(x1) -> c(c(d(x1)))
170.02/43.28	        d(c(x1)) -> c(b(x1))
170.02/43.28	      Restore Modifier:
170.02/43.28	       DPs:
170.02/43.28	        b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	        d#(c(x1)) -> b#(x1)
170.02/43.28	       TRS:
170.02/43.28	        b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	        a(x1) -> c(c(d(x1)))
170.02/43.28	        d(c(x1)) -> c(b(x1))
170.02/43.28	       EDG Processor:
170.02/43.28	        DPs:
170.02/43.28	         b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	         d#(c(x1)) -> b#(x1)
170.02/43.28	        TRS:
170.02/43.28	         b(c(c(x1))) -> a(c(d(x1)))
170.02/43.28	         a(x1) -> c(c(d(x1)))
170.02/43.28	         d(c(x1)) -> c(b(x1))
170.02/43.28	        graph:
170.02/43.28	         d#(c(x1)) -> b#(x1) -> b#(c(c(x1))) -> a#(c(d(x1)))
170.02/43.28	        SCC Processor:
170.02/43.28	         #sccs: 0
170.02/43.28	         #rules: 0
170.02/43.28	         #arcs: 1/4
170.02/43.28	         
170.02/43.29	EOF