39.96/10.58	YES
39.96/10.59	
39.96/10.59	Problem:
39.96/10.59	 strict:
39.96/10.59	  a(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	  c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	 weak:
39.96/10.59	  b(b(a(x1))) -> c(c(c(x1)))
39.96/10.59	  c(b(a(x1))) -> a(c(b(x1)))
39.96/10.59	  b(b(b(x1))) -> b(c(b(x1)))
39.96/10.59	  c(a(a(x1))) -> c(c(a(x1)))
39.96/10.59	
39.96/10.59	Proof:
39.96/10.59	 Arctic Interpretation Processor:
39.96/10.59	  dimension: 1
39.96/10.59	  interpretation:
39.96/10.59	   [b](x0) = 8x0,
39.96/10.59	   
39.96/10.59	   [a](x0) = x0,
39.96/10.59	   
39.96/10.59	   [c](x0) = x0
39.96/10.59	  orientation:
39.96/10.59	   a(a(c(x1))) = x1 >= x1 = a(a(a(x1)))
39.96/10.59	   
39.96/10.59	   c(a(c(x1))) = x1 >= x1 = a(a(a(x1)))
39.96/10.59	   
39.96/10.59	   b(b(a(x1))) = 16x1 >= x1 = c(c(c(x1)))
39.96/10.59	   
39.96/10.59	   c(b(a(x1))) = 8x1 >= 8x1 = a(c(b(x1)))
39.96/10.59	   
39.96/10.59	   b(b(b(x1))) = 24x1 >= 16x1 = b(c(b(x1)))
39.96/10.59	   
39.96/10.59	   c(a(a(x1))) = x1 >= x1 = c(c(a(x1)))
39.96/10.59	  problem:
39.96/10.59	   strict:
39.96/10.59	    a(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	    c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	   weak:
39.96/10.59	    c(b(a(x1))) -> a(c(b(x1)))
39.96/10.59	    c(a(a(x1))) -> c(c(a(x1)))
39.96/10.59	  String Reversal Processor:
39.96/10.59	   strict:
39.96/10.59	    c(a(a(x1))) -> a(a(a(x1)))
39.96/10.59	    c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	   weak:
39.96/10.59	    a(b(c(x1))) -> b(c(a(x1)))
39.96/10.59	    a(a(c(x1))) -> a(c(c(x1)))
39.96/10.59	   Matrix Interpretation Processor: dim=2
39.96/10.59	    
39.96/10.59	    interpretation:
39.96/10.59	                    [0]
39.96/10.59	     [b](x0) = x0 + [3],
39.96/10.59	     
39.96/10.59	               [1 1]  
39.96/10.59	     [a](x0) = [0 1]x0,
39.96/10.59	     
39.96/10.59	               [1 1]  
39.96/10.59	     [c](x0) = [0 1]x0
39.96/10.59	    orientation:
39.96/10.59	                   [1 3]      [1 3]                
39.96/10.59	     c(a(a(x1))) = [0 1]x1 >= [0 1]x1 = a(a(a(x1)))
39.96/10.59	     
39.96/10.59	                   [1 3]      [1 3]                
39.96/10.59	     c(a(c(x1))) = [0 1]x1 >= [0 1]x1 = a(a(a(x1)))
39.96/10.59	     
39.96/10.59	                   [1 2]     [3]    [1 2]     [0]              
39.96/10.59	     a(b(c(x1))) = [0 1]x1 + [3] >= [0 1]x1 + [3] = b(c(a(x1)))
39.96/10.59	     
39.96/10.59	                   [1 3]      [1 3]                
39.96/10.59	     a(a(c(x1))) = [0 1]x1 >= [0 1]x1 = a(c(c(x1)))
39.96/10.59	    problem:
39.96/10.59	     strict:
39.96/10.59	      c(a(a(x1))) -> a(a(a(x1)))
39.96/10.59	      c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	     weak:
39.96/10.59	      a(a(c(x1))) -> a(c(c(x1)))
39.96/10.59	    RT Transformation Processor:
39.96/10.59	     c(a(a(x1))) -> a(a(a(x1)))
39.96/10.59	     c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	     a(a(c(x1))) -> a(c(c(x1)))
39.96/10.59	     DP Processor:
39.96/10.59	      DPs:
39.96/10.59	       c#(a(a(x1))) -> a#(a(a(x1)))
39.96/10.59	       c#(a(c(x1))) -> a#(x1)
39.96/10.59	       c#(a(c(x1))) -> a#(a(x1))
39.96/10.59	       c#(a(c(x1))) -> a#(a(a(x1)))
39.96/10.59	       a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	       a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	      TRS:
39.96/10.59	       c(a(a(x1))) -> a(a(a(x1)))
39.96/10.59	       c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	       a(a(c(x1))) -> a(c(c(x1)))
39.96/10.59	      TDG Processor:
39.96/10.59	       DPs:
39.96/10.59	        c#(a(a(x1))) -> a#(a(a(x1)))
39.96/10.59	        c#(a(c(x1))) -> a#(x1)
39.96/10.59	        c#(a(c(x1))) -> a#(a(x1))
39.96/10.59	        c#(a(c(x1))) -> a#(a(a(x1)))
39.96/10.59	        a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	        a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	       TRS:
39.96/10.59	        c(a(a(x1))) -> a(a(a(x1)))
39.96/10.59	        c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	        a(a(c(x1))) -> a(c(c(x1)))
39.96/10.59	       graph:
39.96/10.59	        a#(a(c(x1))) -> a#(c(c(x1))) -> a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	        a#(a(c(x1))) -> a#(c(c(x1))) -> a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	        a#(a(c(x1))) -> c#(c(x1)) -> c#(a(c(x1))) -> a#(a(a(x1)))
39.96/10.59	        a#(a(c(x1))) -> c#(c(x1)) -> c#(a(c(x1))) -> a#(a(x1))
39.96/10.59	        a#(a(c(x1))) -> c#(c(x1)) -> c#(a(c(x1))) -> a#(x1)
39.96/10.59	        a#(a(c(x1))) -> c#(c(x1)) -> c#(a(a(x1))) -> a#(a(a(x1)))
39.96/10.59	        c#(a(a(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	        c#(a(a(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	        c#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	        c#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	        c#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	        c#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	        c#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	        c#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> c#(c(x1))
39.96/10.59	       Subterm Criterion Processor:
39.96/10.59	        simple projection:
39.96/10.59	         pi(c) = [0,0]
39.96/10.59	         pi(a) = [0,0]
39.96/10.59	         pi(c#) = 0
39.96/10.59	         pi(a#) = 0
39.96/10.59	        problem:
39.96/10.59	         DPs:
39.96/10.59	          c#(a(a(x1))) -> a#(a(a(x1)))
39.96/10.59	          c#(a(c(x1))) -> a#(a(a(x1)))
39.96/10.59	          a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	         TRS:
39.96/10.59	          c(a(a(x1))) -> a(a(a(x1)))
39.96/10.59	          c(a(c(x1))) -> a(a(a(x1)))
39.96/10.59	          a(a(c(x1))) -> a(c(c(x1)))
39.96/10.59	        SCC Processor:
39.96/10.59	         #sccs: 1
39.96/10.59	         #rules: 1
39.96/10.59	         #arcs: 14/9
39.96/10.59	         DPs:
39.96/10.59	          a#(a(c(x1))) -> a#(c(c(x1)))
39.96/10.59	         TRS:
39.96/10.60	          c(a(a(x1))) -> a(a(a(x1)))
39.96/10.60	          c(a(c(x1))) -> a(a(a(x1)))
39.96/10.60	          a(a(c(x1))) -> a(c(c(x1)))
39.96/10.60	         Arctic Interpretation Processor:
39.96/10.60	          dimension: 2
39.96/10.60	          usable rules:
39.96/10.60	           c(a(a(x1))) -> a(a(a(x1)))
39.96/10.60	           c(a(c(x1))) -> a(a(a(x1)))
39.96/10.60	           a(a(c(x1))) -> a(c(c(x1)))
39.96/10.60	          interpretation:
39.96/10.60	           [a#](x0) = [0 0]x0,
39.96/10.60	           
39.96/10.60	                     [0  -&]     [-&]
39.96/10.60	           [a](x0) = [1  -&]x0 + [0 ],
39.96/10.60	           
39.96/10.60	                     [0 0]  
39.96/10.60	           [c](x0) = [0 0]x0
39.96/10.60	          orientation:
39.96/10.60	           a#(a(c(x1))) = [1 1]x1 + [0] >= [0 0]x1 = a#(c(c(x1)))
39.96/10.60	           
39.96/10.60	                         [1  -&]     [0]    [0  -&]     [-&]              
39.96/10.60	           c(a(a(x1))) = [1  -&]x1 + [0] >= [1  -&]x1 + [0 ] = a(a(a(x1)))
39.96/10.60	           
39.96/10.60	                         [1 1]     [0]    [0  -&]     [-&]              
39.96/10.60	           c(a(c(x1))) = [1 1]x1 + [0] >= [1  -&]x1 + [0 ] = a(a(a(x1)))
39.96/10.60	           
39.96/10.60	                         [0 0]     [-&]    [0 0]     [-&]              
39.96/10.60	           a(a(c(x1))) = [1 1]x1 + [0 ] >= [1 1]x1 + [0 ] = a(c(c(x1)))
39.96/10.60	          problem:
39.96/10.60	           DPs:
39.96/10.60	            
39.96/10.60	           TRS:
39.96/10.60	            c(a(a(x1))) -> a(a(a(x1)))
39.96/10.60	            c(a(c(x1))) -> a(a(a(x1)))
39.96/10.60	            a(a(c(x1))) -> a(c(c(x1)))
39.96/10.60	          Qed
39.96/10.60	EOF