167.30/43.03	YES
167.30/43.03	
167.30/43.03	Problem:
167.30/43.03	 a(x1) -> x1
167.30/43.03	 a(x1) -> b(b(x1))
167.30/43.03	 b(a(c(x1))) -> c(c(a(a(x1))))
167.30/43.03	 c(x1) -> x1
167.30/43.03	
167.30/43.03	Proof:
167.30/43.03	 String Reversal Processor:
167.30/43.03	  a(x1) -> x1
167.30/43.03	  a(x1) -> b(b(x1))
167.30/43.03	  c(a(b(x1))) -> a(a(c(c(x1))))
167.30/43.03	  c(x1) -> x1
167.30/43.03	  DP Processor:
167.30/43.03	   DPs:
167.30/43.03	    c#(a(b(x1))) -> c#(x1)
167.30/43.03	    c#(a(b(x1))) -> c#(c(x1))
167.30/43.03	    c#(a(b(x1))) -> a#(c(c(x1)))
167.30/43.03	    c#(a(b(x1))) -> a#(a(c(c(x1))))
167.30/43.03	   TRS:
167.30/43.03	    a(x1) -> x1
167.30/43.03	    a(x1) -> b(b(x1))
167.30/43.03	    c(a(b(x1))) -> a(a(c(c(x1))))
167.30/43.03	    c(x1) -> x1
167.30/43.03	   TDG Processor:
167.30/43.03	    DPs:
167.30/43.03	     c#(a(b(x1))) -> c#(x1)
167.30/43.03	     c#(a(b(x1))) -> c#(c(x1))
167.30/43.03	     c#(a(b(x1))) -> a#(c(c(x1)))
167.30/43.03	     c#(a(b(x1))) -> a#(a(c(c(x1))))
167.30/43.03	    TRS:
167.30/43.03	     a(x1) -> x1
167.30/43.03	     a(x1) -> b(b(x1))
167.30/43.03	     c(a(b(x1))) -> a(a(c(c(x1))))
167.30/43.03	     c(x1) -> x1
167.30/43.03	    graph:
167.30/43.03	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(a(c(c(x1))))
167.30/43.03	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(c(c(x1)))
167.30/43.03	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1))
167.30/43.03	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(x1)
167.30/43.03	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(a(c(c(x1))))
167.30/43.03	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(c(c(x1)))
167.30/43.03	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(c(x1))
167.30/43.03	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(x1)
167.30/43.03	    SCC Processor:
167.30/43.03	     #sccs: 1
167.30/43.03	     #rules: 2
167.30/43.03	     #arcs: 8/16
167.30/43.03	     DPs:
167.30/43.03	      c#(a(b(x1))) -> c#(c(x1))
167.30/43.03	      c#(a(b(x1))) -> c#(x1)
167.30/43.03	     TRS:
167.30/43.03	      a(x1) -> x1
167.30/43.03	      a(x1) -> b(b(x1))
167.30/43.03	      c(a(b(x1))) -> a(a(c(c(x1))))
167.30/43.03	      c(x1) -> x1
167.30/43.03	     Arctic Interpretation Processor:
167.30/43.03	      dimension: 2
167.30/43.03	      usable rules:
167.30/43.03	       a(x1) -> x1
167.30/43.03	       a(x1) -> b(b(x1))
167.30/43.03	       c(a(b(x1))) -> a(a(c(c(x1))))
167.30/43.03	       c(x1) -> x1
167.30/43.03	      interpretation:
167.30/43.03	       [c#](x0) = [0 0]x0 + [0],
167.30/43.03	       
167.30/43.03	                 [0 0]     [-&]
167.30/43.03	       [c](x0) = [0 0]x0 + [2 ],
167.30/43.03	       
167.30/43.03	                 [0 0]     [3]
167.30/43.03	       [b](x0) = [0 0]x0 + [3],
167.30/43.03	       
167.30/43.03	                 [0 0]     [3]
167.30/43.03	       [a](x0) = [1 0]x0 + [3]
167.30/43.03	      orientation:
167.30/43.03	       c#(a(b(x1))) = [1 1]x1 + [4] >= [0 0]x1 + [2] = c#(c(x1))
167.30/43.03	       
167.30/43.03	       c#(a(b(x1))) = [1 1]x1 + [4] >= [0 0]x1 + [0] = c#(x1)
167.30/43.03	       
167.30/43.03	               [0 0]     [3]           
167.30/43.03	       a(x1) = [1 0]x1 + [3] >= x1 = x1
167.30/43.03	       
167.30/43.03	               [0 0]     [3]    [0 0]     [3]           
167.30/43.03	       a(x1) = [1 0]x1 + [3] >= [0 0]x1 + [3] = b(b(x1))
167.30/43.03	       
167.30/43.03	                     [1 1]     [4]    [1 1]     [3]                 
167.30/43.03	       c(a(b(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = a(a(c(c(x1))))
167.30/43.03	       
167.30/43.03	               [0 0]     [-&]           
167.30/43.03	       c(x1) = [0 0]x1 + [2 ] >= x1 = x1
167.30/43.03	      problem:
167.30/43.03	       DPs:
167.30/43.03	        
167.30/43.03	       TRS:
167.30/43.03	        a(x1) -> x1
167.30/43.03	        a(x1) -> b(b(x1))
167.30/43.03	        c(a(b(x1))) -> a(a(c(c(x1))))
167.30/43.03	        c(x1) -> x1
167.30/43.03	      Qed
167.30/43.04	EOF