203.76/45.86	YES
203.76/45.87	
203.76/45.87	Problem:
203.76/45.87	 a(x1) -> x1
203.76/45.87	 a(x1) -> b(b(c(x1)))
203.76/45.87	 c(c(a(x1))) -> a(a(c(c(x1))))
203.76/45.87	
203.76/45.87	Proof:
203.76/45.87	 String Reversal Processor:
203.76/45.87	  a(x1) -> x1
203.76/45.87	  a(x1) -> c(b(b(x1)))
203.76/45.87	  a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	  DP Processor:
203.76/45.87	   DPs:
203.76/45.87	    a#(c(c(x1))) -> a#(x1)
203.76/45.87	    a#(c(c(x1))) -> a#(a(x1))
203.76/45.87	   TRS:
203.76/45.87	    a(x1) -> x1
203.76/45.87	    a(x1) -> c(b(b(x1)))
203.76/45.87	    a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	   Arctic Interpretation Processor:
203.76/45.87	    dimension: 2
203.76/45.87	    usable rules:
203.76/45.87	     a(x1) -> x1
203.76/45.87	     a(x1) -> c(b(b(x1)))
203.76/45.87	     a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	    interpretation:
203.76/45.87	     [a#](x0) = [-& 0 ]x0 + [0],
203.76/45.87	     
203.76/45.87	               [0  0 ]  
203.76/45.87	     [b](x0) = [-& -&]x0,
203.76/45.87	     
203.76/45.87	               [0 1]     [0]
203.76/45.87	     [c](x0) = [0 0]x0 + [3],
203.76/45.87	     
203.76/45.87	               [0 0]     [0]
203.76/45.87	     [a](x0) = [0 0]x0 + [3]
203.76/45.87	    orientation:
203.76/45.87	     a#(c(c(x1))) = [0 1]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1)
203.76/45.87	     
203.76/45.87	     a#(c(c(x1))) = [0 1]x1 + [3] >= [0 0]x1 + [3] = a#(a(x1))
203.76/45.87	     
203.76/45.87	             [0 0]     [0]           
203.76/45.87	     a(x1) = [0 0]x1 + [3] >= x1 = x1
203.76/45.87	     
203.76/45.87	             [0 0]     [0]    [0 0]     [0]              
203.76/45.87	     a(x1) = [0 0]x1 + [3] >= [0 0]x1 + [3] = c(b(b(x1)))
203.76/45.87	     
203.76/45.87	                   [1 1]     [4]    [1 1]     [4]                 
203.76/45.87	     a(c(c(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = c(c(a(a(x1))))
203.76/45.87	    problem:
203.76/45.87	     DPs:
203.76/45.87	      a#(c(c(x1))) -> a#(a(x1))
203.76/45.87	     TRS:
203.76/45.87	      a(x1) -> x1
203.76/45.87	      a(x1) -> c(b(b(x1)))
203.76/45.87	      a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	    Restore Modifier:
203.76/45.87	     DPs:
203.76/45.87	      a#(c(c(x1))) -> a#(a(x1))
203.76/45.87	     TRS:
203.76/45.87	      a(x1) -> x1
203.76/45.87	      a(x1) -> c(b(b(x1)))
203.76/45.87	      a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	     Arctic Interpretation Processor:
203.76/45.87	      dimension: 2
203.76/45.87	      usable rules:
203.76/45.87	       a(x1) -> x1
203.76/45.87	       a(x1) -> c(b(b(x1)))
203.76/45.87	       a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	      interpretation:
203.76/45.87	       [a#](x0) = [2 2]x0 + [0],
203.76/45.87	       
203.76/45.87	                 [0  0 ]     [0 ]
203.76/45.87	       [b](x0) = [-& -&]x0 + [-&],
203.76/45.87	       
203.76/45.87	                 [0 2]     [0]
203.76/45.87	       [c](x0) = [0 0]x0 + [0],
203.76/45.87	       
203.76/45.87	                 [0 0]     [0]
203.76/45.87	       [a](x0) = [0 0]x0 + [0]
203.76/45.87	      orientation:
203.76/45.87	       a#(c(c(x1))) = [4 4]x1 + [4] >= [2 2]x1 + [2] = a#(a(x1))
203.76/45.87	       
203.76/45.87	               [0 0]     [0]           
203.76/45.87	       a(x1) = [0 0]x1 + [0] >= x1 = x1
203.76/45.87	       
203.76/45.87	               [0 0]     [0]    [0 0]     [0]              
203.76/45.87	       a(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(b(b(x1)))
203.76/45.87	       
203.76/45.87	                     [2 2]     [2]    [2 2]     [2]                 
203.76/45.87	       a(c(c(x1))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = c(c(a(a(x1))))
203.76/45.87	      problem:
203.76/45.87	       DPs:
203.76/45.87	        
203.76/45.87	       TRS:
203.76/45.87	        a(x1) -> x1
203.76/45.87	        a(x1) -> c(b(b(x1)))
203.76/45.87	        a(c(c(x1))) -> c(c(a(a(x1))))
203.76/45.87	      Qed
203.76/45.87	EOF