191.45/48.92	YES
191.45/48.93	
191.45/48.93	Problem:
191.45/48.93	 a(a(x1)) -> b(x1)
191.45/48.93	 a(b(x1)) -> c(a(x1))
191.45/48.93	 b(c(x1)) -> c(b(a(x1)))
191.45/48.93	
191.45/48.93	Proof:
191.45/48.93	 String Reversal Processor:
191.45/48.93	  a(a(x1)) -> b(x1)
191.45/48.93	  b(a(x1)) -> a(c(x1))
191.45/48.93	  c(b(x1)) -> a(b(c(x1)))
191.45/48.93	  DP Processor:
191.45/48.93	   DPs:
191.45/48.93	    a#(a(x1)) -> b#(x1)
191.45/48.93	    b#(a(x1)) -> c#(x1)
191.45/48.93	    b#(a(x1)) -> a#(c(x1))
191.45/48.93	    c#(b(x1)) -> c#(x1)
191.45/48.93	    c#(b(x1)) -> b#(c(x1))
191.45/48.93	    c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	   TRS:
191.45/48.93	    a(a(x1)) -> b(x1)
191.45/48.93	    b(a(x1)) -> a(c(x1))
191.45/48.93	    c(b(x1)) -> a(b(c(x1)))
191.45/48.93	   TDG Processor:
191.45/48.93	    DPs:
191.45/48.93	     a#(a(x1)) -> b#(x1)
191.45/48.93	     b#(a(x1)) -> c#(x1)
191.45/48.93	     b#(a(x1)) -> a#(c(x1))
191.45/48.93	     c#(b(x1)) -> c#(x1)
191.45/48.93	     c#(b(x1)) -> b#(c(x1))
191.45/48.93	     c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	    TRS:
191.45/48.93	     a(a(x1)) -> b(x1)
191.45/48.93	     b(a(x1)) -> a(c(x1))
191.45/48.93	     c(b(x1)) -> a(b(c(x1)))
191.45/48.93	    graph:
191.45/48.93	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
191.45/48.93	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
191.45/48.93	     c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(x1))
191.45/48.93	     c#(b(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
191.45/48.93	     c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(x1)
191.45/48.93	     b#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	     b#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
191.45/48.93	     b#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
191.45/48.93	     b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
191.45/48.93	     a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
191.45/48.93	     a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
191.45/48.93	    Arctic Interpretation Processor:
191.45/48.93	     dimension: 2
191.45/48.93	     usable rules:
191.45/48.93	      a(a(x1)) -> b(x1)
191.45/48.93	      b(a(x1)) -> a(c(x1))
191.45/48.93	      c(b(x1)) -> a(b(c(x1)))
191.45/48.93	     interpretation:
191.45/48.93	      [c#](x0) = [0 3]x0,
191.45/48.93	      
191.45/48.93	      [b#](x0) = [0 3]x0 + [0],
191.45/48.93	      
191.45/48.93	      [a#](x0) = [0 3]x0 + [0],
191.45/48.93	      
191.45/48.93	                [0 0]     [0]
191.45/48.93	      [c](x0) = [0 0]x0 + [0],
191.45/48.93	      
191.45/48.93	                [0 0]     [0]
191.45/48.93	      [b](x0) = [1 1]x0 + [2],
191.45/48.93	      
191.45/48.93	                [-& 0 ]     [0]
191.45/48.93	      [a](x0) = [1  0 ]x0 + [2]
191.45/48.93	     orientation:
191.45/48.93	      a#(a(x1)) = [4 3]x1 + [5] >= [0 3]x1 + [0] = b#(x1)
191.45/48.93	      
191.45/48.93	      b#(a(x1)) = [4 3]x1 + [5] >= [0 3]x1 = c#(x1)
191.45/48.93	      
191.45/48.93	      b#(a(x1)) = [4 3]x1 + [5] >= [3 3]x1 + [3] = a#(c(x1))
191.45/48.93	      
191.45/48.93	      c#(b(x1)) = [4 4]x1 + [5] >= [0 3]x1 = c#(x1)
191.45/48.93	      
191.45/48.93	      c#(b(x1)) = [4 4]x1 + [5] >= [3 3]x1 + [3] = b#(c(x1))
191.45/48.93	      
191.45/48.93	      c#(b(x1)) = [4 4]x1 + [5] >= [4 4]x1 + [5] = a#(b(c(x1)))
191.45/48.93	      
191.45/48.93	                 [1 0]     [2]    [0 0]     [0]        
191.45/48.93	      a(a(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b(x1)
191.45/48.93	      
191.45/48.93	                 [1 0]     [2]    [0 0]     [0]           
191.45/48.93	      b(a(x1)) = [2 1]x1 + [3] >= [1 1]x1 + [2] = a(c(x1))
191.45/48.93	      
191.45/48.93	                 [1 1]     [2]    [1 1]     [2]              
191.45/48.93	      c(b(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a(b(c(x1)))
191.45/48.93	     problem:
191.45/48.93	      DPs:
191.45/48.93	       a#(a(x1)) -> b#(x1)
191.45/48.93	       b#(a(x1)) -> c#(x1)
191.45/48.93	       b#(a(x1)) -> a#(c(x1))
191.45/48.93	       c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	      TRS:
191.45/48.93	       a(a(x1)) -> b(x1)
191.45/48.93	       b(a(x1)) -> a(c(x1))
191.45/48.93	       c(b(x1)) -> a(b(c(x1)))
191.45/48.93	     Restore Modifier:
191.45/48.93	      DPs:
191.45/48.93	       a#(a(x1)) -> b#(x1)
191.45/48.93	       b#(a(x1)) -> c#(x1)
191.45/48.93	       b#(a(x1)) -> a#(c(x1))
191.45/48.93	       c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	      TRS:
191.45/48.93	       a(a(x1)) -> b(x1)
191.45/48.93	       b(a(x1)) -> a(c(x1))
191.45/48.93	       c(b(x1)) -> a(b(c(x1)))
191.45/48.93	      EDG Processor:
191.45/48.93	       DPs:
191.45/48.93	        a#(a(x1)) -> b#(x1)
191.45/48.93	        b#(a(x1)) -> c#(x1)
191.45/48.93	        b#(a(x1)) -> a#(c(x1))
191.45/48.93	        c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	       TRS:
191.45/48.93	        a(a(x1)) -> b(x1)
191.45/48.93	        b(a(x1)) -> a(c(x1))
191.45/48.93	        c(b(x1)) -> a(b(c(x1)))
191.45/48.93	       graph:
191.45/48.93	        c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(x1)
191.45/48.93	        b#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
191.45/48.93	        b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
191.45/48.93	        a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
191.45/48.93	        a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
191.45/48.93	       Arctic Interpretation Processor:
191.45/48.93	        dimension: 2
191.45/48.93	        usable rules:
191.45/48.93	         a(a(x1)) -> b(x1)
191.45/48.93	         b(a(x1)) -> a(c(x1))
191.45/48.93	         c(b(x1)) -> a(b(c(x1)))
191.45/48.93	        interpretation:
191.45/48.93	         [c#](x0) = [0 0]x0,
191.45/48.93	         
191.45/48.93	         [b#](x0) = [0 1]x0,
191.45/48.93	         
191.45/48.93	         [a#](x0) = [0  -&]x0,
191.45/48.93	         
191.45/48.93	                   [0  2 ]  
191.45/48.93	         [c](x0) = [-& 0 ]x0,
191.45/48.93	         
191.45/48.93	                   [0 0]     [-&]
191.45/48.93	         [b](x0) = [0 2]x0 + [0 ],
191.45/48.93	         
191.52/48.94	                   [0 2]     [0 ]
191.52/48.94	         [a](x0) = [0 0]x0 + [-&]
191.52/48.94	        orientation:
191.52/48.94	         a#(a(x1)) = [0 2]x1 + [0] >= [0 1]x1 = b#(x1)
191.52/48.94	         
191.52/48.94	         b#(a(x1)) = [1 2]x1 + [0] >= [0 0]x1 = c#(x1)
191.52/48.94	         
191.52/48.94	         b#(a(x1)) = [1 2]x1 + [0] >= [0 2]x1 = a#(c(x1))
191.52/48.94	         
191.52/48.94	         c#(b(x1)) = [0 2]x1 + [0] >= [0 2]x1 = a#(b(c(x1)))
191.52/48.94	         
191.52/48.94	                    [2 2]     [0]    [0 0]     [-&]        
191.52/48.94	         a(a(x1)) = [0 2]x1 + [0] >= [0 2]x1 + [0 ] = b(x1)
191.52/48.94	         
191.52/48.94	                    [0 2]     [0]    [0 2]     [0 ]           
191.52/48.94	         b(a(x1)) = [2 2]x1 + [0] >= [0 2]x1 + [-&] = a(c(x1))
191.52/48.94	         
191.52/48.94	                    [2 4]     [2]    [2 4]     [2]              
191.52/48.94	         c(b(x1)) = [0 2]x1 + [0] >= [0 2]x1 + [0] = a(b(c(x1)))
191.52/48.94	        problem:
191.52/48.94	         DPs:
191.52/48.94	          a#(a(x1)) -> b#(x1)
191.52/48.94	          b#(a(x1)) -> a#(c(x1))
191.52/48.94	          c#(b(x1)) -> a#(b(c(x1)))
191.52/48.94	         TRS:
191.52/48.94	          a(a(x1)) -> b(x1)
191.52/48.94	          b(a(x1)) -> a(c(x1))
191.52/48.94	          c(b(x1)) -> a(b(c(x1)))
191.52/48.94	        Restore Modifier:
191.52/48.94	         DPs:
191.52/48.94	          a#(a(x1)) -> b#(x1)
191.52/48.94	          b#(a(x1)) -> a#(c(x1))
191.52/48.94	          c#(b(x1)) -> a#(b(c(x1)))
191.52/48.94	         TRS:
191.52/48.94	          a(a(x1)) -> b(x1)
191.52/48.94	          b(a(x1)) -> a(c(x1))
191.52/48.94	          c(b(x1)) -> a(b(c(x1)))
191.52/48.94	         EDG Processor:
191.52/48.94	          DPs:
191.52/48.94	           a#(a(x1)) -> b#(x1)
191.52/48.94	           b#(a(x1)) -> a#(c(x1))
191.52/48.94	           c#(b(x1)) -> a#(b(c(x1)))
191.52/48.94	          TRS:
191.52/48.94	           a(a(x1)) -> b(x1)
191.52/48.94	           b(a(x1)) -> a(c(x1))
191.52/48.94	           c(b(x1)) -> a(b(c(x1)))
191.52/48.94	          graph:
191.52/48.94	           c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(x1)
191.52/48.94	           b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
191.52/48.94	           a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
191.52/48.94	          SCC Processor:
191.52/48.94	           #sccs: 1
191.52/48.94	           #rules: 2
191.52/48.94	           #arcs: 3/9
191.52/48.94	           DPs:
191.52/48.94	            a#(a(x1)) -> b#(x1)
191.52/48.94	            b#(a(x1)) -> a#(c(x1))
191.52/48.94	           TRS:
191.52/48.94	            a(a(x1)) -> b(x1)
191.52/48.94	            b(a(x1)) -> a(c(x1))
191.52/48.94	            c(b(x1)) -> a(b(c(x1)))
191.52/48.94	           Arctic Interpretation Processor:
191.52/48.94	            dimension: 2
191.52/48.94	            usable rules:
191.52/48.94	             a(a(x1)) -> b(x1)
191.52/48.94	             b(a(x1)) -> a(c(x1))
191.52/48.94	             c(b(x1)) -> a(b(c(x1)))
191.52/48.94	            interpretation:
191.52/48.94	             [b#](x0) = [1 0]x0,
191.52/48.94	             
191.52/48.94	             [a#](x0) = [0 0]x0,
191.52/48.94	             
191.52/48.94	                       [0 0]  
191.52/48.94	             [c](x0) = [0 0]x0,
191.52/48.94	             
191.52/48.94	                       [0 0]  
191.52/48.94	             [b](x0) = [1 1]x0,
191.52/48.94	             
191.52/48.94	                       [0 0]  
191.52/48.94	             [a](x0) = [1 0]x0
191.52/48.94	            orientation:
191.52/48.94	             a#(a(x1)) = [1 0]x1 >= [1 0]x1 = b#(x1)
191.52/48.94	             
191.52/48.94	             b#(a(x1)) = [1 1]x1 >= [0 0]x1 = a#(c(x1))
191.52/48.94	             
191.52/48.94	                        [1 0]      [0 0]          
191.52/48.94	             a(a(x1)) = [1 1]x1 >= [1 1]x1 = b(x1)
191.52/48.94	             
191.52/48.94	                        [1 0]      [0 0]             
191.52/48.94	             b(a(x1)) = [2 1]x1 >= [1 1]x1 = a(c(x1))
191.52/48.94	             
191.52/48.94	                        [1 1]      [1 1]                
191.52/48.94	             c(b(x1)) = [1 1]x1 >= [1 1]x1 = a(b(c(x1)))
191.52/48.94	            problem:
191.52/48.94	             DPs:
191.52/48.94	              a#(a(x1)) -> b#(x1)
191.52/48.94	             TRS:
191.52/48.94	              a(a(x1)) -> b(x1)
191.52/48.94	              b(a(x1)) -> a(c(x1))
191.52/48.94	              c(b(x1)) -> a(b(c(x1)))
191.52/48.94	            Restore Modifier:
191.52/48.94	             DPs:
191.52/48.94	              a#(a(x1)) -> b#(x1)
191.52/48.94	             TRS:
191.52/48.94	              a(a(x1)) -> b(x1)
191.52/48.94	              b(a(x1)) -> a(c(x1))
191.52/48.94	              c(b(x1)) -> a(b(c(x1)))
191.52/48.94	             EDG Processor:
191.52/48.94	              DPs:
191.52/48.94	               a#(a(x1)) -> b#(x1)
191.52/48.94	              TRS:
191.52/48.94	               a(a(x1)) -> b(x1)
191.52/48.94	               b(a(x1)) -> a(c(x1))
191.52/48.94	               c(b(x1)) -> a(b(c(x1)))
191.52/48.94	              graph:
191.52/48.94	               
191.52/48.94	              SCC Processor:
191.52/48.94	               #sccs: 0
191.52/48.94	               #rules: 0
191.52/48.94	               #arcs: 0/1
191.52/48.94	               
191.52/48.94	EOF