10.31/2.93	YES
10.31/2.93	
10.31/2.93	Problem:
10.31/2.93	 strict:
10.31/2.93	  a(c(a(x1))) -> a(b(b(x1)))
10.31/2.93	  a(c(a(x1))) -> a(c(b(x1)))
10.31/2.93	  a(c(c(x1))) -> b(b(c(x1)))
10.31/2.93	  b(c(a(x1))) -> c(b(a(x1)))
10.31/2.93	 weak:
10.31/2.93	  c(b(c(x1))) -> b(c(c(x1)))
10.31/2.93	  b(b(b(x1))) -> c(a(c(x1)))
10.31/2.93	
10.31/2.93	Proof:
10.31/2.93	 String Reversal Processor:
10.31/2.93	  strict:
10.31/2.93	   a(c(a(x1))) -> b(b(a(x1)))
10.31/2.93	   a(c(a(x1))) -> b(c(a(x1)))
10.31/2.93	   c(c(a(x1))) -> c(b(b(x1)))
10.31/2.93	   a(c(b(x1))) -> a(b(c(x1)))
10.31/2.93	  weak:
10.31/2.93	   c(b(c(x1))) -> c(c(b(x1)))
10.31/2.93	   b(b(b(x1))) -> c(a(c(x1)))
10.31/2.93	  Arctic Interpretation Processor:
10.31/2.93	   dimension: 1
10.31/2.93	   interpretation:
10.31/2.93	    [b](x0) = 1x0,
10.31/2.93	    
10.31/2.93	    [c](x0) = x0,
10.31/2.93	    
10.31/2.93	    [a](x0) = 3x0
10.31/2.93	   orientation:
10.31/2.93	    a(c(a(x1))) = 6x1 >= 5x1 = b(b(a(x1)))
10.31/2.93	    
10.31/2.93	    a(c(a(x1))) = 6x1 >= 4x1 = b(c(a(x1)))
10.31/2.93	    
10.31/2.93	    c(c(a(x1))) = 3x1 >= 2x1 = c(b(b(x1)))
10.31/2.93	    
10.31/2.93	    a(c(b(x1))) = 4x1 >= 4x1 = a(b(c(x1)))
10.31/2.93	    
10.31/2.93	    c(b(c(x1))) = 1x1 >= 1x1 = c(c(b(x1)))
10.31/2.93	    
10.31/2.93	    b(b(b(x1))) = 3x1 >= 3x1 = c(a(c(x1)))
10.31/2.93	   problem:
10.31/2.93	    strict:
10.31/2.93	     a(c(b(x1))) -> a(b(c(x1)))
10.31/2.93	    weak:
10.31/2.93	     c(b(c(x1))) -> c(c(b(x1)))
10.31/2.93	     b(b(b(x1))) -> c(a(c(x1)))
10.31/2.93	   Arctic Interpretation Processor:
10.31/2.93	    dimension: 1
10.31/2.93	    interpretation:
10.31/2.93	     [b](x0) = 9x0,
10.31/2.93	     
10.31/2.93	     [c](x0) = 11x0,
10.31/2.93	     
10.31/2.93	     [a](x0) = 4x0
10.31/2.93	    orientation:
10.31/2.93	     a(c(b(x1))) = 24x1 >= 24x1 = a(b(c(x1)))
10.31/2.93	     
10.31/2.93	     c(b(c(x1))) = 31x1 >= 31x1 = c(c(b(x1)))
10.31/2.93	     
10.31/2.93	     b(b(b(x1))) = 27x1 >= 26x1 = c(a(c(x1)))
10.31/2.93	    problem:
10.31/2.93	     strict:
10.31/2.93	      a(c(b(x1))) -> a(b(c(x1)))
10.31/2.93	     weak:
10.31/2.93	      c(b(c(x1))) -> c(c(b(x1)))
10.31/2.93	    String Reversal Processor:
10.31/2.93	     strict:
10.31/2.93	      b(c(a(x1))) -> c(b(a(x1)))
10.31/2.93	     weak:
10.31/2.93	      c(b(c(x1))) -> b(c(c(x1)))
10.31/2.93	     Bounds Processor:
10.31/2.93	      bound: 1
10.31/2.93	      enrichment: match-rt
10.31/2.93	      automaton:
10.31/2.93	       final states: {4}
10.31/2.93	       transitions:
10.31/2.93	        c1(20) -> 21*
10.31/2.93	        c1(11) -> 12*
10.31/2.93	        c1(13) -> 14*
10.31/2.93	        b1(10) -> 11*
10.31/2.93	        b1(14) -> 15*
10.31/2.93	        a1(9) -> 10*
10.31/2.93	        b0(4) -> 4*
10.31/2.93	        c0(4) -> 4*
10.31/2.93	        a0(4) -> 4*
10.31/2.93	        4 -> 9*
10.31/2.93	        12 -> 13,4
10.31/2.93	        14 -> 20*
10.31/2.93	        15 -> 4*
10.31/2.93	        21 -> 14*
10.31/2.93	      problem:
10.31/2.93	       strict:
10.31/2.93	        
10.31/2.93	       weak:
10.31/2.93	        c(b(c(x1))) -> b(c(c(x1)))
10.31/2.93	      Qed
10.31/2.94	EOF