174.04/43.98	YES
174.04/43.98	
174.04/43.98	Problem:
174.04/43.98	 a(x1) -> b(x1)
174.04/43.98	 b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	 c(c(x1)) -> x1
174.04/43.98	
174.04/43.98	Proof:
174.04/43.98	 DP Processor:
174.04/43.98	  DPs:
174.04/43.98	   a#(x1) -> b#(x1)
174.04/43.98	   b#(b(c(x1))) -> a#(x1)
174.04/43.98	   b#(b(c(x1))) -> a#(a(x1))
174.04/43.98	   b#(b(c(x1))) -> c#(a(a(x1)))
174.04/43.98	   b#(b(c(x1))) -> a#(c(a(a(x1))))
174.04/43.98	   b#(b(c(x1))) -> c#(a(c(a(a(x1)))))
174.04/43.98	  TRS:
174.04/43.98	   a(x1) -> b(x1)
174.04/43.98	   b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	   c(c(x1)) -> x1
174.04/43.98	  TDG Processor:
174.04/43.98	   DPs:
174.04/43.98	    a#(x1) -> b#(x1)
174.04/43.98	    b#(b(c(x1))) -> a#(x1)
174.04/43.98	    b#(b(c(x1))) -> a#(a(x1))
174.04/43.98	    b#(b(c(x1))) -> c#(a(a(x1)))
174.04/43.98	    b#(b(c(x1))) -> a#(c(a(a(x1))))
174.04/43.98	    b#(b(c(x1))) -> c#(a(c(a(a(x1)))))
174.04/43.98	   TRS:
174.04/43.98	    a(x1) -> b(x1)
174.04/43.98	    b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	    c(c(x1)) -> x1
174.04/43.98	   graph:
174.04/43.98	    b#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(x1) -> b#(x1)
174.04/43.98	    b#(b(c(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
174.04/43.98	    b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
174.04/43.98	    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(a(a(x1)))))
174.04/43.98	    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(c(a(a(x1))))
174.04/43.98	    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(a(x1)))
174.04/43.98	    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(a(x1))
174.04/43.98	    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
174.04/43.98	   SCC Processor:
174.04/43.98	    #sccs: 1
174.04/43.98	    #rules: 4
174.04/43.98	    #arcs: 8/36
174.04/43.98	    DPs:
174.04/43.98	     b#(b(c(x1))) -> a#(c(a(a(x1))))
174.04/43.98	     a#(x1) -> b#(x1)
174.04/43.98	     b#(b(c(x1))) -> a#(x1)
174.04/43.98	     b#(b(c(x1))) -> a#(a(x1))
174.04/43.98	    TRS:
174.04/43.98	     a(x1) -> b(x1)
174.04/43.98	     b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	     c(c(x1)) -> x1
174.04/43.98	    Arctic Interpretation Processor:
174.04/43.98	     dimension: 2
174.04/43.98	     usable rules:
174.04/43.98	      a(x1) -> b(x1)
174.04/43.98	      b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	      c(c(x1)) -> x1
174.04/43.98	     interpretation:
174.04/43.98	      [b#](x0) = [1 0]x0 + [0],
174.04/43.98	      
174.04/43.98	      [a#](x0) = [1 0]x0 + [0],
174.04/43.98	      
174.04/43.98	                [-& 0 ]     [0]
174.04/43.98	      [c](x0) = [0  1 ]x0 + [3],
174.04/43.98	      
174.04/43.98	                [-& 0 ]     [0]
174.04/43.98	      [b](x0) = [0  -&]x0 + [2],
174.04/43.98	      
174.04/43.98	                [-& 0 ]     [1]
174.04/43.98	      [a](x0) = [0  -&]x0 + [2]
174.04/43.98	     orientation:
174.04/43.98	      b#(b(c(x1))) = [1 2]x1 + [4] >= [0 1]x1 + [3] = a#(c(a(a(x1))))
174.04/43.98	      
174.04/43.98	      a#(x1) = [1 0]x1 + [0] >= [1 0]x1 + [0] = b#(x1)
174.04/43.98	      
174.04/43.98	      b#(b(c(x1))) = [1 2]x1 + [4] >= [1 0]x1 + [0] = a#(x1)
174.04/43.98	      
174.04/43.98	      b#(b(c(x1))) = [1 2]x1 + [4] >= [0 1]x1 + [2] = a#(a(x1))
174.04/43.98	      
174.04/43.98	              [-& 0 ]     [1]    [-& 0 ]     [0]        
174.04/43.98	      a(x1) = [0  -&]x1 + [2] >= [0  -&]x1 + [2] = b(x1)
174.04/43.98	      
174.04/43.98	                    [-& 0 ]     [2]    [-& 0 ]     [2]                    
174.04/43.98	      b(b(c(x1))) = [0  1 ]x1 + [3] >= [0  1 ]x1 + [3] = c(a(c(a(a(x1)))))
174.04/43.98	      
174.04/43.98	                 [0 1]     [3]           
174.04/43.98	      c(c(x1)) = [1 2]x1 + [4] >= x1 = x1
174.04/43.98	     problem:
174.04/43.98	      DPs:
174.04/43.98	       a#(x1) -> b#(x1)
174.04/43.98	       b#(b(c(x1))) -> a#(x1)
174.04/43.98	      TRS:
174.04/43.98	       a(x1) -> b(x1)
174.04/43.98	       b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	       c(c(x1)) -> x1
174.04/43.98	     Restore Modifier:
174.04/43.98	      DPs:
174.04/43.98	       a#(x1) -> b#(x1)
174.04/43.98	       b#(b(c(x1))) -> a#(x1)
174.04/43.98	      TRS:
174.04/43.98	       a(x1) -> b(x1)
174.04/43.98	       b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	       c(c(x1)) -> x1
174.04/43.98	      EDG Processor:
174.04/43.98	       DPs:
174.04/43.98	        a#(x1) -> b#(x1)
174.04/43.98	        b#(b(c(x1))) -> a#(x1)
174.04/43.98	       TRS:
174.04/43.98	        a(x1) -> b(x1)
174.04/43.98	        b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	        c(c(x1)) -> x1
174.04/43.98	       graph:
174.04/43.98	        b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
174.04/43.98	        a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
174.04/43.98	       Usable Rule Processor:
174.04/43.98	        DPs:
174.04/43.98	         a#(x1) -> b#(x1)
174.04/43.98	         b#(b(c(x1))) -> a#(x1)
174.04/43.98	        TRS:
174.04/43.98	         
174.04/43.98	        Arctic Interpretation Processor:
174.04/43.98	         dimension: 1
174.04/43.98	         usable rules:
174.04/43.98	          
174.04/43.98	         interpretation:
174.04/43.98	          [b#](x0) = x0,
174.04/43.98	          
174.04/43.98	          [a#](x0) = x0,
174.04/43.98	          
174.04/43.98	          [c](x0) = 5x0 + 14,
174.04/43.98	          
174.04/43.98	          [b](x0) = x0 + 0
174.04/43.98	         orientation:
174.04/43.98	          a#(x1) = x1 >= x1 = b#(x1)
174.04/43.98	          
174.04/43.98	          b#(b(c(x1))) = 5x1 + 14 >= x1 = a#(x1)
174.04/43.98	         problem:
174.04/43.98	          DPs:
174.04/43.98	           a#(x1) -> b#(x1)
174.04/43.98	          TRS:
174.04/43.98	           
174.04/43.98	         Restore Modifier:
174.04/43.98	          DPs:
174.04/43.98	           a#(x1) -> b#(x1)
174.04/43.98	          TRS:
174.04/43.98	           a(x1) -> b(x1)
174.04/43.98	           b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	           c(c(x1)) -> x1
174.04/43.98	          EDG Processor:
174.04/43.98	           DPs:
174.04/43.98	            a#(x1) -> b#(x1)
174.04/43.98	           TRS:
174.04/43.98	            a(x1) -> b(x1)
174.04/43.98	            b(b(c(x1))) -> c(a(c(a(a(x1)))))
174.04/43.98	            c(c(x1)) -> x1
174.04/43.98	           graph:
174.04/43.98	            
174.04/43.98	           SCC Processor:
174.04/43.98	            #sccs: 0
174.04/43.98	            #rules: 0
174.04/43.98	            #arcs: 0/1
174.04/43.98	            
174.04/43.99	EOF