191.49/48.64	YES
191.49/48.64	
191.49/48.64	Problem:
191.49/48.64	 a(b(x1)) -> x1
191.49/48.64	 a(c(x1)) -> b(b(x1))
191.49/48.64	 c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	
191.49/48.64	Proof:
191.49/48.64	 DP Processor:
191.49/48.64	  DPs:
191.49/48.64	   c#(b(x1)) -> c#(x1)
191.49/48.64	   c#(b(x1)) -> c#(c(x1))
191.49/48.64	   c#(b(x1)) -> a#(c(c(x1)))
191.49/48.64	   c#(b(x1)) -> a#(a(c(c(x1))))
191.49/48.64	  TRS:
191.49/48.64	   a(b(x1)) -> x1
191.49/48.64	   a(c(x1)) -> b(b(x1))
191.49/48.64	   c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	  TDG Processor:
191.49/48.64	   DPs:
191.49/48.64	    c#(b(x1)) -> c#(x1)
191.49/48.64	    c#(b(x1)) -> c#(c(x1))
191.49/48.64	    c#(b(x1)) -> a#(c(c(x1)))
191.49/48.64	    c#(b(x1)) -> a#(a(c(c(x1))))
191.49/48.64	   TRS:
191.49/48.64	    a(b(x1)) -> x1
191.49/48.64	    a(c(x1)) -> b(b(x1))
191.49/48.64	    c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	   graph:
191.49/48.64	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(c(c(x1))))
191.49/48.64	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(c(c(x1)))
191.49/48.64	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1))
191.49/48.64	    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(x1)
191.49/48.64	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(c(x1))))
191.49/48.64	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(c(x1)))
191.49/48.64	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(c(x1))
191.49/48.64	    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
191.49/48.64	   SCC Processor:
191.49/48.64	    #sccs: 1
191.49/48.64	    #rules: 2
191.49/48.64	    #arcs: 8/16
191.49/48.64	    DPs:
191.49/48.64	     c#(b(x1)) -> c#(c(x1))
191.49/48.64	     c#(b(x1)) -> c#(x1)
191.49/48.64	    TRS:
191.49/48.64	     a(b(x1)) -> x1
191.49/48.64	     a(c(x1)) -> b(b(x1))
191.49/48.64	     c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	    Arctic Interpretation Processor:
191.49/48.64	     dimension: 2
191.49/48.64	     usable rules:
191.49/48.64	      a(b(x1)) -> x1
191.49/48.64	      a(c(x1)) -> b(b(x1))
191.49/48.64	      c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	     interpretation:
191.49/48.64	      [c#](x0) = [0 1]x0,
191.49/48.64	      
191.49/48.64	                [1 2]     [1 ]
191.49/48.64	      [c](x0) = [0 1]x0 + [-&],
191.49/48.64	      
191.49/48.64	                [-& 0 ]     [1]
191.49/48.64	      [a](x0) = [0  -&]x0 + [0],
191.49/48.64	      
191.49/48.64	                [0 0]     [1]
191.49/48.64	      [b](x0) = [0 1]x0 + [0]
191.49/48.64	     orientation:
191.49/48.64	      c#(b(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = c#(c(x1))
191.49/48.64	      
191.49/48.64	      c#(b(x1)) = [1 2]x1 + [1] >= [0 1]x1 = c#(x1)
191.49/48.64	      
191.49/48.64	                 [0 1]     [1]           
191.49/48.64	      a(b(x1)) = [0 0]x1 + [1] >= x1 = x1
191.49/48.64	      
191.49/48.64	                 [0 1]     [1]    [0 1]     [1]           
191.49/48.64	      a(c(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b(b(x1))
191.49/48.64	      
191.49/48.64	                 [2 3]     [2]    [2 3]     [2]                 
191.49/48.64	      c(b(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = a(a(c(c(x1))))
191.49/48.64	     problem:
191.49/48.64	      DPs:
191.49/48.64	       c#(b(x1)) -> c#(c(x1))
191.49/48.64	      TRS:
191.49/48.64	       a(b(x1)) -> x1
191.49/48.64	       a(c(x1)) -> b(b(x1))
191.49/48.64	       c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	     Restore Modifier:
191.49/48.64	      DPs:
191.49/48.64	       c#(b(x1)) -> c#(c(x1))
191.49/48.64	      TRS:
191.49/48.64	       a(b(x1)) -> x1
191.49/48.64	       a(c(x1)) -> b(b(x1))
191.49/48.64	       c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	      EDG Processor:
191.49/48.64	       DPs:
191.49/48.64	        c#(b(x1)) -> c#(c(x1))
191.49/48.64	       TRS:
191.49/48.64	        a(b(x1)) -> x1
191.49/48.64	        a(c(x1)) -> b(b(x1))
191.49/48.64	        c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	       graph:
191.49/48.64	        c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1))
191.49/48.64	       Arctic Interpretation Processor:
191.49/48.64	        dimension: 3
191.49/48.64	        usable rules:
191.49/48.64	         a(b(x1)) -> x1
191.49/48.64	         a(c(x1)) -> b(b(x1))
191.49/48.64	         c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	        interpretation:
191.49/48.64	         [c#](x0) = [-& -& 0 ]x0 + [0],
191.49/48.64	         
191.49/48.64	                   [0  0  0 ]     [-&]
191.49/48.64	         [c](x0) = [0  0  1 ]x0 + [1 ]
191.49/48.64	                   [-& -& 0 ]     [0 ],
191.49/48.64	         
191.49/48.64	                   [0  0  -&]     [0]
191.49/48.64	         [a](x0) = [-& -& 0 ]x0 + [0]
191.49/48.64	                   [0  1  -&]     [0],
191.49/48.64	         
191.49/48.64	                   [-& -& 0 ]     [0 ]
191.49/48.64	         [b](x0) = [0  -& -&]x0 + [-&]
191.49/48.64	                   [0  0  1 ]     [1 ]
191.49/48.64	        orientation:
191.49/48.64	         c#(b(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(c(x1))
191.49/48.64	         
191.49/48.64	                    [0  -& 0 ]     [0]           
191.49/48.64	         a(b(x1)) = [0  0  1 ]x1 + [1] >= x1 = x1
191.49/48.64	                    [1  -& 0 ]     [0]           
191.49/48.64	         
191.49/48.64	                    [0  0  1 ]     [1]    [0  0  1 ]     [1]           
191.49/48.64	         a(c(x1)) = [-& -& 0 ]x1 + [0] >= [-& -& 0 ]x1 + [0] = b(b(x1))
191.49/48.64	                    [1  1  2 ]     [2]    [1  1  2 ]     [2]           
191.49/48.64	         
191.49/48.64	                    [0 0 1]     [1]    [0 0 1]     [1]                 
191.49/48.64	         c(b(x1)) = [1 1 2]x1 + [2] >= [1 1 2]x1 + [2] = a(a(c(c(x1))))
191.49/48.64	                    [0 0 1]     [1]    [0 0 1]     [1]                 
191.49/48.64	        problem:
191.49/48.64	         DPs:
191.49/48.64	          
191.49/48.64	         TRS:
191.49/48.64	          a(b(x1)) -> x1
191.49/48.64	          a(c(x1)) -> b(b(x1))
191.49/48.64	          c(b(x1)) -> a(a(c(c(x1))))
191.49/48.64	        Qed
191.49/48.65	EOF