170.30/43.49	YES
170.30/43.50	
170.30/43.50	Problem:
170.30/43.50	 a(x1) -> b(c(x1))
170.30/43.50	 a(b(b(x1))) -> b(b(a(a(x1))))
170.30/43.50	 c(b(x1)) -> x1
170.30/43.50	
170.30/43.50	Proof:
170.30/43.50	 DP Processor:
170.30/43.50	  DPs:
170.30/43.50	   a#(x1) -> c#(x1)
170.30/43.50	   a#(b(b(x1))) -> a#(x1)
170.30/43.50	   a#(b(b(x1))) -> a#(a(x1))
170.30/43.50	  TRS:
170.30/43.50	   a(x1) -> b(c(x1))
170.30/43.50	   a(b(b(x1))) -> b(b(a(a(x1))))
170.30/43.50	   c(b(x1)) -> x1
170.30/43.50	  TDG Processor:
170.30/43.50	   DPs:
170.30/43.50	    a#(x1) -> c#(x1)
170.30/43.50	    a#(b(b(x1))) -> a#(x1)
170.30/43.50	    a#(b(b(x1))) -> a#(a(x1))
170.30/43.50	   TRS:
170.30/43.50	    a(x1) -> b(c(x1))
170.30/43.50	    a(b(b(x1))) -> b(b(a(a(x1))))
170.30/43.50	    c(b(x1)) -> x1
170.30/43.50	   graph:
170.30/43.50	    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(a(x1))
170.30/43.50	    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(x1)
170.30/43.50	    a#(b(b(x1))) -> a#(a(x1)) -> a#(x1) -> c#(x1)
170.30/43.50	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(a(x1))
170.30/43.50	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
170.30/43.50	    a#(b(b(x1))) -> a#(x1) -> a#(x1) -> c#(x1)
170.30/43.50	   SCC Processor:
170.30/43.50	    #sccs: 1
170.30/43.50	    #rules: 2
170.30/43.50	    #arcs: 6/9
170.30/43.50	    DPs:
170.30/43.50	     a#(b(b(x1))) -> a#(a(x1))
170.30/43.50	     a#(b(b(x1))) -> a#(x1)
170.30/43.50	    TRS:
170.30/43.50	     a(x1) -> b(c(x1))
170.30/43.50	     a(b(b(x1))) -> b(b(a(a(x1))))
170.30/43.50	     c(b(x1)) -> x1
170.30/43.50	    Arctic Interpretation Processor:
170.30/43.50	     dimension: 2
170.30/43.50	     usable rules:
170.30/43.50	      a(x1) -> b(c(x1))
170.30/43.50	      a(b(b(x1))) -> b(b(a(a(x1))))
170.30/43.50	      c(b(x1)) -> x1
170.30/43.50	     interpretation:
170.30/43.50	      [a#](x0) = [3 1]x0,
170.30/43.50	      
170.30/43.50	                [0 0]     [0]
170.30/43.50	      [b](x0) = [1 0]x0 + [2],
170.30/43.50	      
170.30/43.50	                [0  -&]     [-&]
170.30/43.50	      [c](x0) = [0  -&]x0 + [0 ],
170.30/43.50	      
170.30/43.50	                [0  -&]     [0]
170.30/43.50	      [a](x0) = [1  0 ]x0 + [2]
170.30/43.50	     orientation:
170.30/43.50	      a#(b(b(x1))) = [4 3]x1 + [5] >= [3 1]x1 + [3] = a#(a(x1))
170.30/43.50	      
170.30/43.50	      a#(b(b(x1))) = [4 3]x1 + [5] >= [3 1]x1 = a#(x1)
170.30/43.50	      
170.30/43.50	              [0  -&]     [0]    [0  -&]     [0]           
170.30/43.50	      a(x1) = [1  0 ]x1 + [2] >= [1  -&]x1 + [2] = b(c(x1))
170.30/43.50	      
170.30/43.50	                    [1 0]     [2]    [1 0]     [2]                 
170.30/43.50	      a(b(b(x1))) = [2 1]x1 + [3] >= [2 1]x1 + [3] = b(b(a(a(x1))))
170.30/43.50	      
170.30/43.50	                 [0 0]     [0]           
170.30/43.50	      c(b(x1)) = [0 0]x1 + [0] >= x1 = x1
170.30/43.50	     problem:
170.30/43.50	      DPs:
170.30/43.50	       
170.30/43.50	      TRS:
170.30/43.50	       a(x1) -> b(c(x1))
170.30/43.50	       a(b(b(x1))) -> b(b(a(a(x1))))
170.30/43.50	       c(b(x1)) -> x1
170.30/43.50	     Qed
170.30/43.50	EOF