173.67/43.32	YES
174.02/43.32	
174.02/43.32	Problem:
174.02/43.32	 a(x1) -> x1
174.02/43.32	 a(x1) -> b(x1)
174.02/43.32	 a(c(x1)) -> c(c(a(b(x1))))
174.02/43.32	 b(b(x1)) -> a(x1)
174.02/43.32	
174.02/43.32	Proof:
174.02/43.32	 String Reversal Processor:
174.02/43.32	  a(x1) -> x1
174.02/43.32	  a(x1) -> b(x1)
174.02/43.32	  c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	  b(b(x1)) -> a(x1)
174.02/43.32	  DP Processor:
174.02/43.32	   DPs:
174.02/43.32	    a#(x1) -> b#(x1)
174.02/43.32	    c#(a(x1)) -> c#(x1)
174.02/43.32	    c#(a(x1)) -> c#(c(x1))
174.02/43.32	    c#(a(x1)) -> a#(c(c(x1)))
174.02/43.32	    c#(a(x1)) -> b#(a(c(c(x1))))
174.02/43.32	    b#(b(x1)) -> a#(x1)
174.02/43.32	   TRS:
174.02/43.32	    a(x1) -> x1
174.02/43.32	    a(x1) -> b(x1)
174.02/43.32	    c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	    b(b(x1)) -> a(x1)
174.02/43.32	   TDG Processor:
174.02/43.32	    DPs:
174.02/43.32	     a#(x1) -> b#(x1)
174.02/43.32	     c#(a(x1)) -> c#(x1)
174.02/43.32	     c#(a(x1)) -> c#(c(x1))
174.02/43.32	     c#(a(x1)) -> a#(c(c(x1)))
174.02/43.32	     c#(a(x1)) -> b#(a(c(c(x1))))
174.02/43.32	     b#(b(x1)) -> a#(x1)
174.02/43.32	    TRS:
174.02/43.32	     a(x1) -> x1
174.02/43.32	     a(x1) -> b(x1)
174.02/43.32	     c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	     b(b(x1)) -> a(x1)
174.02/43.32	    graph:
174.02/43.32	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(a(c(c(x1))))
174.02/43.32	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(c(c(x1)))
174.02/43.32	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
174.02/43.32	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1)
174.02/43.32	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(c(x1))))
174.02/43.32	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(c(x1)))
174.02/43.32	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1))
174.02/43.32	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
174.02/43.32	     c#(a(x1)) -> b#(a(c(c(x1)))) -> b#(b(x1)) -> a#(x1)
174.02/43.32	     c#(a(x1)) -> a#(c(c(x1))) -> a#(x1) -> b#(x1)
174.02/43.32	     b#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
174.02/43.32	     a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(x1)
174.02/43.32	    SCC Processor:
174.02/43.32	     #sccs: 2
174.02/43.32	     #rules: 4
174.02/43.32	     #arcs: 12/36
174.02/43.32	     DPs:
174.02/43.32	      c#(a(x1)) -> c#(c(x1))
174.02/43.32	      c#(a(x1)) -> c#(x1)
174.02/43.32	     TRS:
174.02/43.32	      a(x1) -> x1
174.02/43.32	      a(x1) -> b(x1)
174.02/43.32	      c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	      b(b(x1)) -> a(x1)
174.02/43.32	     Arctic Interpretation Processor:
174.02/43.32	      dimension: 2
174.02/43.32	      usable rules:
174.02/43.32	       a(x1) -> x1
174.02/43.32	       a(x1) -> b(x1)
174.02/43.32	       c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	       b(b(x1)) -> a(x1)
174.02/43.32	      interpretation:
174.02/43.32	       [c#](x0) = [0 0]x0,
174.02/43.32	       
174.02/43.32	                 [0  0 ]  
174.02/43.32	       [c](x0) = [-& 0 ]x0,
174.02/43.32	       
174.02/43.32	                 [0 0]     [-&]
174.02/43.32	       [b](x0) = [1 0]x0 + [0 ],
174.02/43.32	       
174.02/43.32	                 [0 0]     [-&]
174.02/43.32	       [a](x0) = [1 1]x0 + [0 ]
174.02/43.32	      orientation:
174.02/43.32	       c#(a(x1)) = [1 1]x1 + [0] >= [0 0]x1 = c#(c(x1))
174.02/43.32	       
174.02/43.32	       c#(a(x1)) = [1 1]x1 + [0] >= [0 0]x1 = c#(x1)
174.02/43.32	       
174.02/43.32	               [0 0]     [-&]           
174.02/43.32	       a(x1) = [1 1]x1 + [0 ] >= x1 = x1
174.02/43.32	       
174.02/43.32	               [0 0]     [-&]    [0 0]     [-&]        
174.02/43.32	       a(x1) = [1 1]x1 + [0 ] >= [1 0]x1 + [0 ] = b(x1)
174.02/43.32	       
174.02/43.32	                  [1 1]     [0]    [1 1]     [0]                 
174.02/43.32	       c(a(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = b(a(c(c(x1))))
174.02/43.32	       
174.02/43.32	                  [1 0]     [0]    [0 0]     [-&]        
174.02/43.32	       b(b(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0 ] = a(x1)
174.02/43.32	      problem:
174.02/43.32	       DPs:
174.02/43.32	        
174.02/43.32	       TRS:
174.02/43.32	        a(x1) -> x1
174.02/43.32	        a(x1) -> b(x1)
174.02/43.32	        c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	        b(b(x1)) -> a(x1)
174.02/43.32	      Qed
174.02/43.32	     
174.02/43.32	     DPs:
174.02/43.32	      a#(x1) -> b#(x1)
174.02/43.32	      b#(b(x1)) -> a#(x1)
174.02/43.32	     TRS:
174.02/43.32	      a(x1) -> x1
174.02/43.32	      a(x1) -> b(x1)
174.02/43.32	      c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	      b(b(x1)) -> a(x1)
174.02/43.32	     Usable Rule Processor:
174.02/43.32	      DPs:
174.02/43.32	       a#(x1) -> b#(x1)
174.02/43.32	       b#(b(x1)) -> a#(x1)
174.02/43.32	      TRS:
174.02/43.32	       
174.02/43.32	      Arctic Interpretation Processor:
174.02/43.32	       dimension: 1
174.02/43.32	       usable rules:
174.02/43.32	        
174.02/43.32	       interpretation:
174.02/43.32	        [b#](x0) = x0,
174.02/43.32	        
174.02/43.32	        [a#](x0) = x0,
174.02/43.32	        
174.02/43.32	        [b](x0) = 5x0 + 9
174.02/43.32	       orientation:
174.02/43.32	        a#(x1) = x1 >= x1 = b#(x1)
174.02/43.32	        
174.02/43.32	        b#(b(x1)) = 5x1 + 9 >= x1 = a#(x1)
174.02/43.32	       problem:
174.02/43.32	        DPs:
174.02/43.32	         a#(x1) -> b#(x1)
174.02/43.32	        TRS:
174.02/43.32	         
174.02/43.32	       Restore Modifier:
174.02/43.32	        DPs:
174.02/43.32	         a#(x1) -> b#(x1)
174.02/43.32	        TRS:
174.02/43.32	         a(x1) -> x1
174.02/43.32	         a(x1) -> b(x1)
174.02/43.32	         c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	         b(b(x1)) -> a(x1)
174.02/43.32	        EDG Processor:
174.02/43.32	         DPs:
174.02/43.32	          a#(x1) -> b#(x1)
174.02/43.32	         TRS:
174.02/43.32	          a(x1) -> x1
174.02/43.32	          a(x1) -> b(x1)
174.02/43.32	          c(a(x1)) -> b(a(c(c(x1))))
174.02/43.32	          b(b(x1)) -> a(x1)
174.02/43.32	         graph:
174.02/43.32	          
174.02/43.32	         SCC Processor:
174.02/43.32	          #sccs: 0
174.02/43.32	          #rules: 0
174.02/43.32	          #arcs: 0/1
174.02/43.32	          
174.02/43.33	EOF