164.53/42.20	YES
165.40/42.21	
165.40/42.21	Problem:
165.40/42.21	 a(b(x1)) -> x1
165.40/42.21	 a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	 b(c(x1)) -> a(b(x1))
165.40/42.21	
165.40/42.21	Proof:
165.40/42.21	 DP Processor:
165.40/42.21	  DPs:
165.40/42.21	   a#(c(x1)) -> b#(c(x1))
165.40/42.21	   b#(c(x1)) -> b#(x1)
165.40/42.21	   b#(c(x1)) -> a#(b(x1))
165.40/42.21	  TRS:
165.40/42.21	   a(b(x1)) -> x1
165.40/42.21	   a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	   b(c(x1)) -> a(b(x1))
165.40/42.21	  TDG Processor:
165.40/42.21	   DPs:
165.40/42.21	    a#(c(x1)) -> b#(c(x1))
165.40/42.21	    b#(c(x1)) -> b#(x1)
165.40/42.21	    b#(c(x1)) -> a#(b(x1))
165.40/42.21	   TRS:
165.40/42.21	    a(b(x1)) -> x1
165.40/42.21	    a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	    b(c(x1)) -> a(b(x1))
165.40/42.21	   graph:
165.40/42.21	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1))
165.40/42.21	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
165.40/42.21	    b#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(c(x1))
165.40/42.21	    a#(c(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(b(x1))
165.40/42.21	    a#(c(x1)) -> b#(c(x1)) -> b#(c(x1)) -> b#(x1)
165.40/42.21	   Arctic Interpretation Processor:
165.40/42.21	    dimension: 1
165.40/42.21	    usable rules:
165.40/42.21	     a(b(x1)) -> x1
165.40/42.21	     a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	     b(c(x1)) -> a(b(x1))
165.40/42.21	    interpretation:
165.40/42.21	     [b#](x0) = x0 + 8,
165.40/42.21	     
165.40/42.21	     [a#](x0) = x0 + 0,
165.40/42.21	     
165.40/42.21	     [c](x0) = 1x0 + 8,
165.40/42.21	     
165.40/42.21	     [a](x0) = 1x0 + 4,
165.40/42.21	     
165.40/42.21	     [b](x0) = -1x0 + 0
165.40/42.21	    orientation:
165.40/42.21	     a#(c(x1)) = 1x1 + 8 >= 1x1 + 8 = b#(c(x1))
165.40/42.21	     
165.40/42.21	     b#(c(x1)) = 1x1 + 8 >= x1 + 8 = b#(x1)
165.40/42.21	     
165.40/42.21	     b#(c(x1)) = 1x1 + 8 >= -1x1 + 0 = a#(b(x1))
165.40/42.21	     
165.40/42.21	     a(b(x1)) = x1 + 4 >= x1 = x1
165.40/42.21	     
165.40/42.21	     a(c(x1)) = 2x1 + 9 >= 2x1 + 9 = c(c(b(c(x1))))
165.40/42.21	     
165.40/42.21	     b(c(x1)) = x1 + 7 >= x1 + 4 = a(b(x1))
165.40/42.21	    problem:
165.40/42.21	     DPs:
165.40/42.21	      a#(c(x1)) -> b#(c(x1))
165.40/42.21	      b#(c(x1)) -> b#(x1)
165.40/42.21	     TRS:
165.40/42.21	      a(b(x1)) -> x1
165.40/42.21	      a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	      b(c(x1)) -> a(b(x1))
165.40/42.21	    Restore Modifier:
165.40/42.21	     DPs:
165.40/42.21	      a#(c(x1)) -> b#(c(x1))
165.40/42.21	      b#(c(x1)) -> b#(x1)
165.40/42.21	     TRS:
165.40/42.21	      a(b(x1)) -> x1
165.40/42.21	      a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	      b(c(x1)) -> a(b(x1))
165.40/42.21	     EDG Processor:
165.40/42.21	      DPs:
165.40/42.21	       a#(c(x1)) -> b#(c(x1))
165.40/42.21	       b#(c(x1)) -> b#(x1)
165.40/42.21	      TRS:
165.40/42.21	       a(b(x1)) -> x1
165.40/42.21	       a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	       b(c(x1)) -> a(b(x1))
165.40/42.21	      graph:
165.40/42.21	       b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
165.40/42.21	       a#(c(x1)) -> b#(c(x1)) -> b#(c(x1)) -> b#(x1)
165.40/42.21	      SCC Processor:
165.40/42.21	       #sccs: 1
165.40/42.21	       #rules: 1
165.40/42.21	       #arcs: 2/4
165.40/42.21	       DPs:
165.40/42.21	        b#(c(x1)) -> b#(x1)
165.40/42.21	       TRS:
165.40/42.21	        a(b(x1)) -> x1
165.40/42.21	        a(c(x1)) -> c(c(b(c(x1))))
165.40/42.21	        b(c(x1)) -> a(b(x1))
165.40/42.21	       Usable Rule Processor:
165.40/42.21	        DPs:
165.40/42.21	         b#(c(x1)) -> b#(x1)
165.40/42.21	        TRS:
165.40/42.21	         
165.40/42.21	        Arctic Interpretation Processor:
165.40/42.21	         dimension: 4
165.40/42.21	         usable rules:
165.40/42.21	          
165.40/42.21	         interpretation:
165.40/42.21	          [b#](x0) = [0  -& -& -&]x0,
165.40/42.21	          
165.40/42.21	                    [1 0 0 0]     [0]
165.40/42.21	                    [0 0 0 0]     [0]
165.40/42.21	          [c](x0) = [1 0 0 0]x0 + [0]
165.40/42.21	                    [0 0 0 0]     [0]
165.40/42.21	         orientation:
165.40/42.21	          b#(c(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = b#(x1)
165.40/42.21	         problem:
165.40/42.21	          DPs:
165.40/42.21	           
165.40/42.21	          TRS:
165.40/42.21	           
165.40/42.21	         Qed
165.40/42.21	EOF