167.71/42.85	YES
167.71/42.86	
167.71/42.86	Problem:
167.71/42.86	 a(x1) -> x1
167.71/42.86	 a(x1) -> b(x1)
167.71/42.86	 a(c(b(x1))) -> c(c(a(a(x1))))
167.71/42.86	 c(x1) -> b(x1)
167.71/42.86	
167.71/42.86	Proof:
167.71/42.86	 DP Processor:
167.71/42.86	  DPs:
167.71/42.86	   a#(c(b(x1))) -> a#(x1)
167.71/42.86	   a#(c(b(x1))) -> a#(a(x1))
167.71/42.86	   a#(c(b(x1))) -> c#(a(a(x1)))
167.71/42.86	   a#(c(b(x1))) -> c#(c(a(a(x1))))
167.71/42.86	  TRS:
167.71/42.86	   a(x1) -> x1
167.71/42.86	   a(x1) -> b(x1)
167.71/42.86	   a(c(b(x1))) -> c(c(a(a(x1))))
167.71/42.86	   c(x1) -> b(x1)
167.71/42.86	  TDG Processor:
167.71/42.86	   DPs:
167.71/42.86	    a#(c(b(x1))) -> a#(x1)
167.71/42.86	    a#(c(b(x1))) -> a#(a(x1))
167.71/42.86	    a#(c(b(x1))) -> c#(a(a(x1)))
167.71/42.86	    a#(c(b(x1))) -> c#(c(a(a(x1))))
167.71/42.86	   TRS:
167.71/42.86	    a(x1) -> x1
167.71/42.86	    a(x1) -> b(x1)
167.71/42.86	    a(c(b(x1))) -> c(c(a(a(x1))))
167.71/42.86	    c(x1) -> b(x1)
167.71/42.86	   graph:
167.71/42.86	    a#(c(b(x1))) -> a#(a(x1)) -> a#(c(b(x1))) -> c#(c(a(a(x1))))
167.71/42.86	    a#(c(b(x1))) -> a#(a(x1)) -> a#(c(b(x1))) -> c#(a(a(x1)))
167.71/42.86	    a#(c(b(x1))) -> a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1))
167.71/42.86	    a#(c(b(x1))) -> a#(a(x1)) -> a#(c(b(x1))) -> a#(x1)
167.71/42.86	    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> c#(c(a(a(x1))))
167.71/42.86	    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> c#(a(a(x1)))
167.71/42.86	    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(a(x1))
167.71/42.86	    a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(x1)
167.71/42.86	   SCC Processor:
167.71/42.86	    #sccs: 1
167.71/42.86	    #rules: 2
167.71/42.86	    #arcs: 8/16
167.71/42.86	    DPs:
167.71/42.86	     a#(c(b(x1))) -> a#(a(x1))
167.71/42.86	     a#(c(b(x1))) -> a#(x1)
167.71/42.86	    TRS:
167.71/42.86	     a(x1) -> x1
167.71/42.86	     a(x1) -> b(x1)
167.71/42.86	     a(c(b(x1))) -> c(c(a(a(x1))))
167.71/42.86	     c(x1) -> b(x1)
167.71/42.86	    Arctic Interpretation Processor:
167.71/42.86	     dimension: 2
167.71/42.86	     usable rules:
167.71/42.86	      a(x1) -> x1
167.71/42.86	      a(x1) -> b(x1)
167.71/42.86	      a(c(b(x1))) -> c(c(a(a(x1))))
167.71/42.86	      c(x1) -> b(x1)
167.71/42.86	     interpretation:
167.71/42.86	      [a#](x0) = [0 0]x0 + [0],
167.71/42.86	      
167.71/42.86	                [0 2]     [0]
167.71/42.86	      [c](x0) = [0 0]x0 + [3],
167.71/42.86	      
167.71/42.86	                [0 0]     [-&]
167.71/42.86	      [b](x0) = [0 0]x0 + [3 ],
167.71/42.86	      
167.71/42.86	                [0 0]     [-&]
167.71/42.86	      [a](x0) = [0 0]x0 + [3 ]
167.71/42.86	     orientation:
167.71/42.86	      a#(c(b(x1))) = [2 2]x1 + [5] >= [0 0]x1 + [3] = a#(a(x1))
167.71/42.86	      
167.71/42.86	      a#(c(b(x1))) = [2 2]x1 + [5] >= [0 0]x1 + [0] = a#(x1)
167.71/42.86	      
167.71/42.86	              [0 0]     [-&]           
167.71/42.86	      a(x1) = [0 0]x1 + [3 ] >= x1 = x1
167.71/42.86	      
167.71/42.86	              [0 0]     [-&]    [0 0]     [-&]        
167.71/42.86	      a(x1) = [0 0]x1 + [3 ] >= [0 0]x1 + [3 ] = b(x1)
167.71/42.86	      
167.71/42.86	                    [2 2]     [5]    [2 2]     [5]                 
167.71/42.86	      a(c(b(x1))) = [2 2]x1 + [5] >= [2 2]x1 + [5] = c(c(a(a(x1))))
167.71/42.86	      
167.71/42.86	              [0 2]     [0]    [0 0]     [-&]        
167.71/42.86	      c(x1) = [0 0]x1 + [3] >= [0 0]x1 + [3 ] = b(x1)
167.71/42.86	     problem:
167.71/42.86	      DPs:
167.71/42.86	       
167.71/42.86	      TRS:
167.71/42.86	       a(x1) -> x1
167.71/42.86	       a(x1) -> b(x1)
167.71/42.86	       a(c(b(x1))) -> c(c(a(a(x1))))
167.71/42.86	       c(x1) -> b(x1)
167.71/42.86	     Qed
167.71/42.86	EOF