166.19/42.44	YES
166.19/42.45	
166.19/42.45	Problem:
166.19/42.45	 a(x1) -> x1
166.19/42.45	 a(x1) -> b(x1)
166.19/42.45	 b(a(c(x1))) -> c(c(a(a(x1))))
166.19/42.45	 c(x1) -> b(x1)
166.19/42.45	
166.19/42.45	Proof:
166.19/42.45	 String Reversal Processor:
166.19/42.45	  a(x1) -> x1
166.19/42.45	  a(x1) -> b(x1)
166.19/42.45	  c(a(b(x1))) -> a(a(c(c(x1))))
166.19/42.45	  c(x1) -> b(x1)
166.19/42.45	  DP Processor:
166.19/42.45	   DPs:
166.19/42.45	    c#(a(b(x1))) -> c#(x1)
166.19/42.45	    c#(a(b(x1))) -> c#(c(x1))
166.19/42.45	    c#(a(b(x1))) -> a#(c(c(x1)))
166.19/42.45	    c#(a(b(x1))) -> a#(a(c(c(x1))))
166.19/42.45	   TRS:
166.19/42.45	    a(x1) -> x1
166.19/42.45	    a(x1) -> b(x1)
166.19/42.45	    c(a(b(x1))) -> a(a(c(c(x1))))
166.19/42.45	    c(x1) -> b(x1)
166.19/42.45	   TDG Processor:
166.19/42.45	    DPs:
166.19/42.45	     c#(a(b(x1))) -> c#(x1)
166.19/42.45	     c#(a(b(x1))) -> c#(c(x1))
166.19/42.45	     c#(a(b(x1))) -> a#(c(c(x1)))
166.19/42.45	     c#(a(b(x1))) -> a#(a(c(c(x1))))
166.19/42.45	    TRS:
166.19/42.45	     a(x1) -> x1
166.19/42.45	     a(x1) -> b(x1)
166.19/42.45	     c(a(b(x1))) -> a(a(c(c(x1))))
166.19/42.45	     c(x1) -> b(x1)
166.19/42.45	    graph:
166.19/42.45	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(a(c(c(x1))))
166.19/42.45	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(c(c(x1)))
166.19/42.45	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1))
166.19/42.45	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(x1)
166.19/42.45	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(a(c(c(x1))))
166.19/42.45	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(c(c(x1)))
166.19/42.45	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(c(x1))
166.19/42.45	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(x1)
166.19/42.45	    SCC Processor:
166.19/42.45	     #sccs: 1
166.19/42.45	     #rules: 2
166.19/42.45	     #arcs: 8/16
166.19/42.45	     DPs:
166.19/42.45	      c#(a(b(x1))) -> c#(c(x1))
166.19/42.45	      c#(a(b(x1))) -> c#(x1)
166.19/42.45	     TRS:
166.19/42.45	      a(x1) -> x1
166.19/42.45	      a(x1) -> b(x1)
166.19/42.45	      c(a(b(x1))) -> a(a(c(c(x1))))
166.19/42.45	      c(x1) -> b(x1)
166.19/42.45	     Arctic Interpretation Processor:
166.19/42.45	      dimension: 2
166.19/42.45	      usable rules:
166.19/42.45	       a(x1) -> x1
166.19/42.45	       a(x1) -> b(x1)
166.19/42.45	       c(a(b(x1))) -> a(a(c(c(x1))))
166.19/42.45	       c(x1) -> b(x1)
166.19/42.45	      interpretation:
166.19/42.45	       [c#](x0) = [-& 3 ]x0 + [0],
166.19/42.45	       
166.19/42.45	                 [-& 1 ]     [0]
166.19/42.45	       [c](x0) = [-& 0 ]x0 + [0],
166.19/42.45	       
166.19/42.45	                 [-& 1 ]     [0]
166.19/42.45	       [b](x0) = [-& -&]x0 + [0],
166.19/42.45	       
166.19/42.45	                 [0 1]     [0]
166.19/42.45	       [a](x0) = [0 0]x0 + [1]
166.19/42.45	      orientation:
166.19/42.45	       c#(a(b(x1))) = [-& 4 ]x1 + [4] >= [-& 3 ]x1 + [3] = c#(c(x1))
166.19/42.45	       
166.19/42.45	       c#(a(b(x1))) = [-& 4 ]x1 + [4] >= [-& 3 ]x1 + [0] = c#(x1)
166.19/42.45	       
166.19/42.45	               [0 1]     [0]           
166.19/42.45	       a(x1) = [0 0]x1 + [1] >= x1 = x1
166.19/42.45	       
166.19/42.45	               [0 1]     [0]    [-& 1 ]     [0]        
166.19/42.45	       a(x1) = [0 0]x1 + [1] >= [-& -&]x1 + [0] = b(x1)
166.19/42.45	       
166.19/42.45	                     [-& 2 ]     [2]    [-& 2 ]     [2]                 
166.19/42.45	       c(a(b(x1))) = [-& 1 ]x1 + [1] >= [-& 1 ]x1 + [1] = a(a(c(c(x1))))
166.19/42.45	       
166.19/42.45	               [-& 1 ]     [0]    [-& 1 ]     [0]        
166.19/42.45	       c(x1) = [-& 0 ]x1 + [0] >= [-& -&]x1 + [0] = b(x1)
166.19/42.45	      problem:
166.19/42.45	       DPs:
166.19/42.45	        
166.19/42.45	       TRS:
166.19/42.45	        a(x1) -> x1
166.19/42.45	        a(x1) -> b(x1)
166.19/42.45	        c(a(b(x1))) -> a(a(c(c(x1))))
166.19/42.45	        c(x1) -> b(x1)
166.19/42.45	      Qed
166.19/42.45	EOF