180.57/46.15	YES
180.57/46.15	
180.57/46.15	Problem:
180.57/46.15	 a(x1) -> b(x1)
180.57/46.15	 a(b(x1)) -> x1
180.57/46.15	 c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	
180.57/46.15	Proof:
180.57/46.15	 DP Processor:
180.57/46.15	  DPs:
180.57/46.15	   c#(c(b(x1))) -> c#(x1)
180.57/46.15	   c#(c(b(x1))) -> c#(c(x1))
180.57/46.15	   c#(c(b(x1))) -> a#(c(c(x1)))
180.57/46.15	   c#(c(b(x1))) -> c#(a(c(c(x1))))
180.57/46.15	  TRS:
180.57/46.15	   a(x1) -> b(x1)
180.57/46.15	   a(b(x1)) -> x1
180.57/46.15	   c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	  TDG Processor:
180.57/46.15	   DPs:
180.57/46.15	    c#(c(b(x1))) -> c#(x1)
180.57/46.15	    c#(c(b(x1))) -> c#(c(x1))
180.57/46.15	    c#(c(b(x1))) -> a#(c(c(x1)))
180.57/46.15	    c#(c(b(x1))) -> c#(a(c(c(x1))))
180.57/46.15	   TRS:
180.57/46.15	    a(x1) -> b(x1)
180.57/46.15	    a(b(x1)) -> x1
180.57/46.15	    c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	   graph:
180.57/46.15	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
180.57/46.15	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(c(x1)))
180.57/46.15	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1))
180.57/46.15	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1)
180.57/46.15	    c#(c(b(x1))) -> c#(a(c(c(x1)))) ->
180.57/46.15	    c#(c(b(x1))) -> c#(a(c(c(x1))))
180.57/46.15	    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> a#(c(c(x1)))
180.57/46.15	    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(c(x1))
180.57/46.15	    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(x1)
180.57/46.15	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
180.57/46.15	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1)))
180.57/46.15	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1))
180.57/46.15	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
180.57/46.15	   SCC Processor:
180.57/46.15	    #sccs: 1
180.57/46.15	    #rules: 3
180.57/46.15	    #arcs: 12/16
180.57/46.15	    DPs:
180.57/46.15	     c#(c(b(x1))) -> c#(c(x1))
180.57/46.15	     c#(c(b(x1))) -> c#(x1)
180.57/46.15	     c#(c(b(x1))) -> c#(a(c(c(x1))))
180.57/46.15	    TRS:
180.57/46.15	     a(x1) -> b(x1)
180.57/46.15	     a(b(x1)) -> x1
180.57/46.15	     c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	    Arctic Interpretation Processor:
180.57/46.15	     dimension: 2
180.57/46.15	     usable rules:
180.57/46.15	      a(x1) -> b(x1)
180.57/46.15	      a(b(x1)) -> x1
180.57/46.15	      c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	     interpretation:
180.57/46.15	      [c#](x0) = [0 2]x0 + [0],
180.57/46.15	      
180.57/46.15	                [-& 0 ]     [0]
180.57/46.15	      [c](x0) = [0  -&]x0 + [0],
180.57/46.15	      
180.57/46.15	                [1  0 ]     [1 ]
180.57/46.15	      [b](x0) = [-& -&]x0 + [-&],
180.57/46.15	      
180.57/46.15	                [1  0 ]     [1]
180.57/46.15	      [a](x0) = [0  -&]x0 + [0]
180.57/46.15	     orientation:
180.57/46.15	      c#(c(b(x1))) = [3 2]x1 + [3] >= [2 0]x1 + [2] = c#(c(x1))
180.57/46.15	      
180.57/46.15	      c#(c(b(x1))) = [3 2]x1 + [3] >= [0 2]x1 + [0] = c#(x1)
180.57/46.15	      
180.57/46.15	      c#(c(b(x1))) = [3 2]x1 + [3] >= [2 0]x1 + [2] = c#(a(c(c(x1))))
180.57/46.15	      
180.57/46.15	              [1  0 ]     [1]    [1  0 ]     [1 ]        
180.57/46.15	      a(x1) = [0  -&]x1 + [0] >= [-& -&]x1 + [-&] = b(x1)
180.57/46.15	      
180.57/46.15	                 [2 1]     [2]           
180.57/46.15	      a(b(x1)) = [1 0]x1 + [1] >= x1 = x1
180.57/46.15	      
180.57/46.15	                    [1  0 ]     [1]    [1  0 ]     [1 ]                    
180.57/46.15	      c(c(b(x1))) = [-& -&]x1 + [0] >= [-& -&]x1 + [-&] = b(c(a(c(c(x1)))))
180.57/46.15	     problem:
180.57/46.15	      DPs:
180.57/46.15	       c#(c(b(x1))) -> c#(x1)
180.57/46.15	      TRS:
180.57/46.15	       a(x1) -> b(x1)
180.57/46.15	       a(b(x1)) -> x1
180.57/46.15	       c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	     Restore Modifier:
180.57/46.15	      DPs:
180.57/46.15	       c#(c(b(x1))) -> c#(x1)
180.57/46.15	      TRS:
180.57/46.15	       a(x1) -> b(x1)
180.57/46.15	       a(b(x1)) -> x1
180.57/46.15	       c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	      EDG Processor:
180.57/46.15	       DPs:
180.57/46.15	        c#(c(b(x1))) -> c#(x1)
180.57/46.15	       TRS:
180.57/46.15	        a(x1) -> b(x1)
180.57/46.15	        a(b(x1)) -> x1
180.57/46.15	        c(c(b(x1))) -> b(c(a(c(c(x1)))))
180.57/46.15	       graph:
180.57/46.15	        c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
180.57/46.15	       Usable Rule Processor:
180.57/46.15	        DPs:
180.57/46.15	         c#(c(b(x1))) -> c#(x1)
180.57/46.15	        TRS:
180.57/46.15	         
180.57/46.15	        Arctic Interpretation Processor:
180.57/46.15	         dimension: 2
180.57/46.15	         usable rules:
180.57/46.15	          
180.57/46.15	         interpretation:
180.57/46.15	          [c#](x0) = [0  -&]x0,
180.57/46.15	          
180.57/46.15	                    [0  3 ]     [0]
180.57/46.15	          [c](x0) = [3  -&]x0 + [0],
180.57/46.15	          
180.57/46.15	                    [0 2]     [1 ]
180.57/46.15	          [b](x0) = [0 3]x0 + [-&]
180.57/46.15	         orientation:
180.57/46.15	          c#(c(b(x1))) = [3 6]x1 + [1] >= [0  -&]x1 = c#(x1)
180.57/46.15	         problem:
180.57/46.15	          DPs:
180.57/46.15	           
180.57/46.15	          TRS:
180.57/46.15	           
180.57/46.15	         Qed
180.57/46.16	EOF